Derivative Rules

Relative maximum/minimum

Local maximum/minimum

Absolute maximum/minimum

Global maximum/minimum

How do you find critical points?

f’ = 0 OR f’ is und

How do you tell is f(x) is increasing or decreasing?

f’ > 0 increasing f’ < 0 decreasing

How do you tell if f’(x) is increasing or decreasing?

f’’ > 0 increasing f’’ < 0 decreasing

How do you find a relative maximum? (First derivative test)

f’ changes from positive → negative

How do you find relative minimum? (first derivative test)

f’ changes from negative → positive

What is extrema?

Maximum / minimum

How do you find absolute extrema?

1- critical points

2- end points

f(x) is concave up when:

f’ is increasing OR f’’ > 0

f(x) is concave down when:

f’ is decreasing OR f’’ < 0

How do you find inflection points?

f’’ changes signs

How do you find relative maximum? (Second derivative test)

f’(c) = 0 AND f’’(c) < 0

How do you find relative minimum? (Second derivative test)

f’(c) = 0 AND f’’(c) > 0