Stage 36 · Limits, Derivatives & Their Applications
36.5.1 The Sign of the Derivative and Increasing or Decreasing
36.5 The Derivative as a Spotlight: Studying How Functions Behave
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36.5.1 The Sign of the Derivative and Increasing or Decreasing
Core ideaWhen the steepness points up (f′>0) you're climbing, and when it points down (f′<0) you're descending.
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.