AP Calc

Question 1

Definition of a derivative

Answer 1

1. Lim as h approaches zero of (f(x+h) - f(x)/h

2. Lim as x approaches a of (f(x) - f(a)) / (x-a)

Question 2

Differentiability and continuity

Answer 2

If f is differentiable at a, then f is continuous at a. The converse to the Theorem is false ( f(x) = |x| ).

Question 3

mean value theorem

Answer 3

The slope of the curve will equal the average value of the curve at some point within the interval.

Question 4

Antiderivative

Answer 4

Indefinite integral