3. First and second derivative rules (2.2)

First derivative rule

If f'(a) > 0 then f(x) is increasing at x = a.

If f'(a) < 0 then f(x) is decreasing at x = a.

Second derivative rule

If f''(a) > 0 then f(x) is concave up at x = a.

If f''(a) < 0 then f(x) is concave down at x = a.

If f''(a) = 0 then don't use this rule!

Graphs for the key derivative cases.

Graphs, and graphs of their derivatives.