# Unit 5 Vocabulary Crossword

Type
Crossword
Description

If f'(x)>0, then f is
If f''(x) changes from positive to negative, then f has a(n) _________ point
If f(x)>0, then f is ___ the x-axis
If f'(x)<0, then f is
If f''(x)>0, then f'(x) is
If f''(x)>0, then f(x) is
If f''(x)<0, then f'(x) is
If f''(x)<0, then f(x) is
If f'(c)=0, then c is a ________ point
If f'(x) is increasing, then f is
If f''(x)<0, then f'(x) is
If f''(c)=0, then c is a _____ point
f'(x) changes from positive to negative makes a _____ maximum on f
If f''(x) changes from positive to negative, then f changes ______
a relative ______ is when f changes from decreasing to increasing

## Calculus Word Search

Type
Word Search
Description

Antidifferentiation
Differentiability
Absolute Maximum
Absolute Minimum
Antiderivative
Discontinuity
Local Extrema
Quotient Rule
Acceleration
Concave Down
Riemann Sum
Chain Rule
Concave Up
Continuous
Derivative
Asymptote
Factorial
Hyperbola
Logarithm
Limit

## Calculus Crossword Puzzle

Type
Crossword
Description

It is the greatest value of f(x) over a defined interval of x, provided y=f(x).
It is the least value of f(x) over a defined interval of x, provided y=f(x).
The original function of a derivative.
A line (or curve) that a function approaches without actually reaching the line.
It is the second letter of the Greek alphabet.
A basic rule in calculus to find the derivative of a composite function.
If a graph has no gaps, no holes, no steps, or discontinuities it is...
An integral between limits of integration is a...
It is the fourth letter of the Greek alphabet.
It is the slope of the line tangent to a function.
A function that is continuous is...
When a function is not continuous it has...
An integral with no limits of integration.
When a curve changes direction.
Speed and direction is also...

## Calculus Crossword

Type
Crossword
Description

The highest point on a graph, especially over a specified domain
The lowest point on a graph, especially over a specified domain
Given a function with a derivative, the antiderivative of that derivative function returns the original function.
a basic rule in calculus to find the derivative of a composite function
When approximating an integral in calculus we may treat each partition as a Trapezoid to determine the area under the curve.
A Derivative taken of a first Derivative
A simple device in calculus to determine the derivative of a monomial.
An algorithm within the calculus to find the derivative of the Product of two functions.
adheres to this property: f(-x) = -f(x).
derivative of a constant
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.
If f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined)
Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 some
The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.
[(f'(x) g(x)) - ((f(x) g'(x))] / (g(x))^2
A change in concavity
derivative of sin(x).
derivative of cos(x).
derivative of ln(x)
derivative of csc(x).
derivative of sec(x).
(y₂-y₁)/(x₂-x₁)
switch x and y

## coordinate geometry Crossword

Type
Crossword
Description

another name of coordinate plane
x-axis is also known as
the coordinates of points are of the form of (+,-) is in which quadrant
the famous mathematician associated with the problems of describing the position of a point in a plane
(0,0) are the coordinates of
point (-1,7_2) lies in which quadrant
the x coordinate of a point lies in the third quadrant is always
if the abscissa of a point is 1 and the ordinate is 0, then the point lies in the
the abscissa of all points on the y axis is always
for a given point P _ _____ is the distance of the point P from x axis respectievely
what will be the distance of the point (0,-3) from the origin
Rene Descartes was a ______ mathematician
if x and y both are positive , then the point (x,y) lies in _____ quadrant
by plotting the points o(0,0)

Type
Crossword
Description

the opposite of distributing
Ax^2+Bx+C
b^2-4ac =0
b^2-4ac>0
b^2-4ac<0
used to find the zeros(roots,x-intercepts,solutions)to a quadratic equation.
roots, x-intercepts and solutions
b^2 -4ac
Ax^2+Bx+C=0
numbers that is multiplied by a variable
the shape of the graph of a quadratic function
the peak in the curve
where a<0
where a>0
when the discriminant is negative
when the squared number is a negatve
where the parabola hits
when Ax^2+Bx+C does not equal 0
cannot change in equation
line of symmetry of a parabola

## Calculus Review Crossword

Type
Crossword
Description

What weren't we allowed to use on tests?
The instantaneous rate of change will equal the mean rate of change somewhere in the interval
a line that intersects a curve only once
the slope of a tangent line
the slope of a vertical line
the rate of change with respect to x
a line segment intersecting two lines
the relative maximum and minimum points of the parent function
tells us max/min, increasing/decreasing intervals, slope of tan line, velocity
when the function changes concavity
the derivative of speed
the derivative of velocity
rate at a specific moment
where does a derivative not exist
the rate over a time interval
the absolute value of velocity
what is it called when velocity is moving backwards
how can you tell if a function is concave up or down
the lowest point of a function
a line or curve that the graph follows closely but never touches
the highest point of a function
when there is a range on a function or set of numbers
an interval that contains its endpoints
when the graph of a function is continuous
a function that moves upward from left to right
a function obtained by switching the x and y variables in a function
does not include its endpoints
the set of x-values for which a functon is defined
rates if change are related by differentiation

Type
Crossword
Description

one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
2. a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
simplify expressions, simplify fractions, and solve equations
4. an equation containing a single variable of degree 2
5. is a number used to multiply a variabl
6. number is a value that, when multiplied by itself, gives the number
7.a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit
8.the highest or lowest point, also known as the maximum or minimum of a parabola.
9.the point at which the graph of an equation crosses the x-axis.
10. A line through a shape so that each side is a mirror image.
11. A mathematical expression that is the sum of three monomials
12. An expression that has a square root, cube root, etc.
13. one that when squared gives a negative result
14. where you change the sign in the middle of two terms
15. a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number
16.a technique used to solve quadratic equations, graph quadratic functions, and evaluate integrals
17. another way of writing the equation of a line.
18. the value of a function at a certain point in its domain, which is greater than or equal to the values at all other points in the immediate vicinity of the point
19. the place where the graph has a vertex at its lowest point
20. members x of the domain of f such that f(x) vanishes at x

Type
Crossword
Description

f(x) ; in form of __________________
a point/curved line equidistant to focus/directrix
__________________, used for parabolas
the solutions to a quadratic equation
A perfect square, for example __________________
a number that includes both a real and imaginary number.
putting the constant on the other side of the equation to make a perfect/factorable trinomial.
a bad boy couldn't decide whether or not to go to a raaaadical house party, he didn't want to be square and miss out on 4 awesome chicks. The party ended at 2 am. (__________________)
y=__________________ ; gives you number of solutions
where the axis of symmetry passes through, minimum/maximum in parabola. (written as coordinate)
where the line intercepts the x-axis.
the solutions to the quadratic formula
the x-value of the vertex, line that hits the parabola (line makes parabola symmetrical)
__________________=0
y=__________________ ; translations to find vertex
when a is negative, y-value of vertex, highest point on the parabola
when a is positive, y-value of vertex, lowest point on the parabola
an expression with three terms
symbol: _______ ; used to find perfect squares (ex. 8x8=64, ______)
when the discriminant is negative
when the discriminant is positive
when the discriminant is 0
Square root of negative number; _____
what is multiplied to the variable, x

## Calc BC Cross Word Puzzle

Type
Crossword
Description

The highest point on a graph, especially over a specified domain. It is the greatest value of f(x) over a defined interval of x, provided y=f(x). ( f'(x)=0 , f''(x)<0 )
The lowest point on a graph, especially over a specified domain. It is the least value of f(x) over a defined interval of x, provided y=f(x). (f'(x)=0 , f''(x)>0 )
A line (or curve) that a function approaches without actually reaching the line as the domain either grows unbounded or approaches a limit.
when the sum of their expanded terms reaches a boundary or limit.
Let f be defined at c. If f'(c)=0 or if f' is undefined at c, what is c?
A function f has this at (c,f(c)). if f''(c)=0 or f''(c) does not exist and if f'' changes sign from positive to negative or negative to positive at x=c or if f'(x) changes from increasing to decreasing or decreasing to increasing at x=c
If an object moves along a straight line with position function s(t), then its this is v(t)=s'(t)
If an object moves along a straight line with position function s(t), then its this is |v(t)|
If an object moves along a straight line with position function s(t), then its this is a(t)=v'(t)=s''(t)
s= ∫ sqrt(1+[f'(x)]^2) dx on the bounds of a to b. What is this formula for?
If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f'(c)=(f(b)-f(a))/(b-a)
If f is continuous on [a,b] and k is any number between f(a) and f(b), then there is at least one number c between a and b such that f(c)=k
In a rational funcion, the graph appears to approach thee horizontal line y=c, as x approaching infinity or negative infinity. In this case, what is y=c?
In a rational function, this asymptote occurs when a factor remains in the denominator.
In a rational function, this asymptote occurs when the power of x in the numerator is greater than the power of x in the denominator.
this of the function f(x) at x=a is defined as f'(a)= lim(h approaching to 0) (f(a+h)-f(a))/h
The derivative using this rule is (d/dx)x^n=nx^(n-1) where n is any real number
suppose that f and g are differentiable at x. then (d/dx)[f(x)g(x)]= f'(x)g(x)+f(x)g'(X). what is this rule's name?
suppose that f and g are differentiable at x and g(x) is not equal to 0. Then (d/dx)[f(x)/g(x)]= (f'(x)g(x)-f(x)g'(x))/(g(x))^2. What's this rule's name?
When f(x)>=g(x) on the interval [a,b], then the ? between these two curves in the given interval is ∫ [f(x)-g(x)]dx (bounded a to b)
When V= ∫ pi[(outer radius)^2-(inner radius)^2]dx (bounded a to b) What method is this?
S= 2pi∫ f(x){sqrt(1+[f'(x)]^2)} dx on the bounds of a to b. What is this formula for?
A situation where population growth levels off and approaches a limiting number M ( the carrying capacity) because of limited resources is called this.
graphical approach, also called 'direction fields'. Pick several points (x,y) and sketch a tiny segment with slope as specified by dy/dx. It shows the general shape of all solutions.
Numerical approximation to the solution to a differential equation. Arithmetic way of following the lines in a slope field. Use the point slope form to find an approximation value. Given an initial value, and an indicated step size, along with the DE, we can solve for the solution. What method is this?
the process of finding the greatest or least value of a function for some constraint, which must be true regardless of the solution. This finds the most suitable value for a function within a given domain.
If the limit does not exist, we say that the improper integral ____.
This coordinate system is a two-dimensional system where each point is represented as a distance r from the origin (sometimes called the pole) and an angle θ from the positive horizontal axis.
This series diverges if |r|>=1. If |r|<1, the series converges to the sum S=a/(1-r). _____ series.
This series is a series whose terms are alternately positive and negative. ____ series.

Type
Crossword
Description

the minimum or maximum point of a parabola
where the parabola crosses the x-axis
where the parabola crosses the y-axis
vertical line that splits the parabola in half
the form of the equation: y = a(x-b)(x-c)
the form of the equation: y = a(x-h)^2+k
the form of the equation: y = ax^2+bx+c
the shape of a quadratic graph
the highest point on a concave down parabola
the lowest point on a concave up parabola
another name for x-intercepts