AP Calculus – Chapter 3 - Derivatives
AP Calculus – Chapter 3 - DerivativesWhen f ′(a) fails to exist Where the tangent does not exist:points of discontinuity (function does not exist)at cornersat cuspsAlso at vertical tangents (slope is undefined)Theorems If f has a derivative at x = a, then f is continuous at x = a. Intermediate Value Theorem (IVT): If a & b are any two points in an interval on which f is continuous, then f MUST take on every value between f(a) & f(b). Intermediate Value Theorem for derivatives: If a & b are any two points in an interval on which f is differentiable, then f ′ MUST take on every value between f ′(a) & f ′(b).Note: A function can be continuous but not differentiable but if it is differentiable it has to be continuousFinding the Derivative Power Rule:Sum and Difference rules:f(x)= 3x2 + 5x – 12 f(x) = -8x-2 – 5x3+ 2xAP style questions: ................
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