Increasing and decreasing functions, the first derivative test and absolute extrema

Learning objectives

Determine the intervals on which a function is increasing or decreasing from the sign of f′, using a sign chart with critical points and points where f′ is undefined as boundaries

Apply the first derivative test to classify each critical point as a local maximum, a local minimum or neither, and write a justification that refers to the sign change of f′

Find the absolute extrema of a continuous function on a closed interval with the candidates test, comparing the function values at the critical points and at the endpoints

Find absolute extrema on an open or unbounded interval, including the case where a single critical point must be the absolute extremum

Read information about the increasing and decreasing behavior and extrema of f from a graph of f′ rather than of f, and justify conclusions using the correct calculus language