AP Calculus - Ultimate Justifications Guide

Front

To justify that f is continuous at x = a

Back

Front

To justify that f is differentiable at x = a

Back

Front

To justify that f is increasing on the interval (a, b)

Back

State/show that f' > 0 on the interval (a, b)

Front

To justify that f is decreasing on the interval (a, b)

Back

State/show that f' < 0 on the interval (a, b)

Front

To justify that f has a critical point at x = a

Back

State/show that f'(a) = 0 or undefined

Front

To justify that f has a relative minimum at x = a

Back

State/show that f' changes from negative to positive at x = a

Front

To justify that f has a relative maximum at x = a

Back

State/show that f' changes from positive to negative at x = a

Front

To justify that f is concave up on the interval (a, b)

Back

State/show that f'' > 0 on the interval (a, b)

Front

To justify that f is concave down on the interval (a, b)

Back

State/show that f'' < 0 on the interval (a, b)

Front

To justify that f has an inflection point at x = a

Back

State/show that f''(a) = 0 or undefined and f'' changes signs