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AP CALCULUS AB REVIEW
Chapter 2
Differentiation
Definition of Tangent Line with Slop m
If f is defined on an open interval containing c, and if the limit
lim∆x→0∆y∆x= lim∆x→0fc+∆x-f(c)∆x=m
exists, then the line passing through (c, f(c)) with slope m is the tangent line to the graph of f at the point (c, f(c)).
Definition of the Derivative of a Function
The Derivative of f at x is given by
f'x= lim∆x→0fc+∆x-f(c)∆x
provided the limit exists. For all x for which this limit exists, f’ is a function of x.
*The Power Rule
*The Product Rule
*ddxsinx= cosx
*ddxcosx= -sinx
*The Chain Rule
☺Implicit Differentiation (take the derivative on both sides; derivative of y is y*y’)
Chapter 3
Applications of Differentiation
*Extrema and the first derivative test (minimum: − → + , maximum: + → − , + & − are the sign of f’(x) )
*Definition of a Critical Number
Let f be defined at c. If f’(c) = 0 OR IF F IS NOT DIFFERENTIABLE AT C, then c is a critical number of f.
*Rolle’s Theorem
If f is differentiable on the open interval (a, b) and f (a) = f (b), then there is at least one number c in (a, b) such that f’(c) = 0.
*The Mean Value Theo