Stage 36 · Limits, Derivatives & Their Applications
36.5.3 Extrema: Peaks and Valleys
36.5 The Derivative as a Spotlight: Studying How Functions Behave
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36.5.3 Extrema: Peaks and Valleys
Core ideaTurning from uphill to downhill gives a peak, the reverse gives a valley, and at the turn f′=0.
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.