Stage 36 · Limits, Derivatives & Their Applications
36.5.5 Extremes on a Closed Interval
36.5 The Derivative as a Spotlight: Studying How Functions Behave
Point 5 of 6
36.5.5 Extremes on a Closed Interval
Core ideaThe overall highest and lowest can only sit at a peak, a valley, or one of the two endpoints, so just compare them one by one.
Module goal. Read a function's rise and fall from the sign of its derivative, pin down its peaks, valleys, and extremes, and see the shape of a curve at a glance.