Second Derivative Test for Concavity of a Function
Let the function y = f(x) have a second derivative on the interval (a, b). - If f''(x) > 0, then the curve y = f(x) is concave up on (a, b). - If f''(x) < 0, t…
Syllabus path: Functions › Preliminary Derivatives › Applications of Derivatives
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CSCA Mathematics Formula Reference
Formula and explanation
Let the function y = f(x) have a second derivative on the interval (a, b). - If f''(x) > 0, then the curve y = f(x) is concave up on (a, b). - If f''(x) < 0, then the curve y = f(x) is concave down on (a, b). Inflection point: A point where the concavity changes. Points where f''(x) = 0 or f''(x) does not exist are candidates for inflection points.
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Applications of Derivatives
Applications of Derivatives 1. Core Logic & Visualization The derivative f'(x) acts as a "barometer" for the function f(x), indicating its trend: Sign of f'(x) Monotonicity (Increasing/Decreasing) Zeros of f'(x) Extrema (Max/Min points) | Sign of f'(x) | Behavior of f(x) | Visual…
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