Calculus Crossword

when f'(x) is increasing, f(x) is concave __
-1/rad(1-x^2) is the derivative of ______
the derivative of displacement is ______
the integral of the absolute value of v(t) from a to b is the _________ traveled by the particle from time t=a to time t=b
if a function you want to optimize has 1+ variables, use _______ to rewrite the function
the volume of a sphere is related to its ________
extrema occur when f'(x) is 0 or _________
the integral of acceleration is __________
__________ is the math of change
for a limit to exist, the limit from the right must _____ the limit from the left
if a function is differentiable, it is also ________
points of inflection occur when f"(x) changes ______
tanx is the ________ of (secx)^2
the integral of 1/x(dx) = ___________
if velocity is positive and acceleration is negative, the speed of the particle is _________
when finding the volume by rotating around the x or y axis and there is a gap between the function and the axis, use the ________ method
by ________ rule, if the limit as x goes to a of f(x)/g(x) is of the indeterminate form, take the derivative of the numerator and the denominator
a continuous function has no _____ or jumps
if f(2)=3, then f^-1(3)= _____
if g(x) is the ________ of f(x), then g'(x)=1/f'(g(x))
holes in the graph are ________ discontinuity
if f(x) is continuous on [a,b] and f(a)<0 and f(b)>0, then by the ____________ theorem, there must be some value, c, on [a,b] where f(c)=0
________ functions do not have points of inflection
if the position function X(t) is concave up and _______, speed of the particle is increasing at time t
________ rule states that to take the derivative of f(x)=uv, one must set f'(x)=u'v+uv'
if the integral of f(x) from a to b is _______, the integral of f(x) from b to a will be positive
f^(4)(sinx)= _____
if f(a)=f(b), at some point between a and b, f'(x)= ______, given f(x) is continuous and differentiable on (a,b)
to find the __________ of a function using a calculator, graph the derivative of the function and find the roots
another name for absolute extrema values is ________ extrema
functions are not differentiable at ______ on the graph
the integral is also referred to as the ____________
__________ is the world's greatest calculus teacher
V=rad3/4 times the integral from a to b of [f(x)]^2 is the formula for finding the volume of a solid with ___________ triangle cross sections perpendicular to the x axis
v=pi/8 times the integral from a to b of [f(x)-g(x)]^2 is how one finds the volume using _____ cross sections
if f(x)=(x^3-5)^4, one would need to use _____ rule to find the derivative
to differentiate f(x)=u/v, one would need to use _______ rule
if a function is concave down, the tangent line lies _____ the curve
if a function is decreasing and concave down, then LRAM is an __________
f'(a) is the slope of the line ______ to f(x) at x=a
if f(x) is the rate at which water is flowing into a tank and g(x) is the rate at which water is leaking out of the tank, then if the integral from 0 to t of f(x) is greater than the integral from 0 to t of g(x), at time t the amount of water in the tank is _________
0/0 or infinity/infinity is the _________ form of a limit
if f(x) is ________ and concave up at x=a, f"(x)>f'(x) at x=a
________ show the derivative of a function at given coordinates on a graph
________ differentiation is used when a function contains both x and y
_________ theorem is a specific case of the Mean Value Theorem
Mean Value Theorem says that at some point on the closed interval [a,b], given f(x) is continuous and differentiable over (a,b), the slope of the tangent line at a point c, equals the slope of the _____ line from a to b
_________ can be used if one wanted to determine the minimum amount of material needed to build a fence of specified dimensions
limits can be found both _______ and graphically
if f"(x) does not _____ signs at a critical value, there is not a point of inflection at this critical value