The highest point on a graph, especially over a specified domain
Absolute Maximum
The lowest point on a graph, especially over a specified domain
Absolute Minimum
Given a function with a derivative, the antiderivative of that derivative function returns the original function.
Antiderivative
a basic rule in calculus to find the derivative of a composite function
Chain Rule
When approximating an integral in calculus we may treat each partition as a Trapezoid to determine the area under the curve.
Trapezoidal Rule
A Derivative taken of a first Derivative
Second Derivative
A simple device in calculus to determine the derivative of a monomial.
Power Rule
An algorithm within the calculus to find the derivative of the Product of two functions.
Product Rule
adheres to this property: f(-x) = -f(x).
Odd Function
derivative of a constant
Zero
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.
Extreme Value Theorem
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)
Critical Number
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
Rolle's Theorem
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.
Mean Value Theorem
[(f'(x) g(x)) - ((f(x) g'(x))] / (g(x))^2
Quotient Rule
A change in concavity
Inflection Point
derivative of sin(x).
cos(x)
derivative of cos(x).
-sin(x)
derivative of ln(x)
1/x
derivative of csc(x).
-csc(x)cot(x)
derivative of sec(x).
sec(x)tan(x)
(y₂-y₁)/(x₂-x₁)
Slope
switch x and y
inverse function