AP CALC AB EXAM MUST KNOWS EXAM QUESTIONS WITH CORRECT ANSWERS

AP CALC AB EXAM MUST KNOWS
EXAM QUESTIONS WITH CORRECT
ANSWERS
Intermediate Value Theorem - ANSWER-If f is continuous on [a,b] and k is a number
between f(a) and f(b), then there exists at least one number c such that f(c)=k

Mean Value Theorem - ANSWER-if f(x) is continuous and differentiable, slope of
tangent line equals slope of secant line at least once in the interval (a, b)

f '(c) = [f(b) - f(a)]/(b - a)

How to find the critical points - ANSWER-1. set the d/dx=0
2. find the x value
3. plug the x value back into the original equation to find the y

How to find the inflection points - ANSWER-set the second derivative = to 0

How to find the derivative of an inverse - ANSWER-1. Set the equation = to the given
value
2. Take the derivative of the given equation and put it under 1
3. Plug the x vlaue you got from step 1
h'(x)=(1/f'(h(x))

Derivative of loga(x) - ANSWER-1/xlna

Disk Method - ANSWER-V= int: pi[f(x)]^2 dx

Washer Method - ANSWER-V = pi (integral) R^2-r^2 dx

1 - ANSWER-lim as x->0 of sinx/x

0 - ANSWER-lim as x->0 of 1-cosx/x

1 - ANSWER-lim as x->0 tanx/x

Area of equilateral triangle - ANSWER-(s^2x root3)/4

derivative of y=a^f(x) - ANSWER-y'= a^f(x) x f'(x) x ln(a)
Derivative of arcsin(x) - ANSWER-1/sqrt(1-x^2)

Derivative of arccos(x) - ANSWER--1/sqrt(1-x^2)