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{ Ch. 5 Review: Integrals AP Calculus

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5.2: The Differential dy 5.2: Linear Approximation 5.3: Indefinite Integrals 5.4: Riemann Sums (Definite Integrals) 5.5: Mean Value Theorem/Rolle’s Theorem Ch. 5 Test Topics

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The Differential dy Tangent line

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Linear Approximation

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If a function is continuous and differentiable on the interval [a, b], then there is at least one point x = c at which the slope of the tangent equals the slope of the secant connecting f(a) and f(b) Mean Value Theorem

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If a function f is: 1) Differentiable for all values of x in the open interval (a, b) and 2) Continuous for all values of x in the closed interval [a, b] Then there is at least one number x = c in (a, b) such that Mean Value Theorem (MVT)

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If a function is differentiable and continuous on the interval [a, b], and f(a) = f(b) = 0, then there is at least one value x = c such that f’(c) = 0. Rolle’s Theorem

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Remember – Function must be CONTINUOUS and DIFFERENTIABLE on interval! Otherwise, conclusion of MVT may not be met. Mean Value Theorem

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Integrals Self-Quiz

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R Problems, pg. 260: R1 –R5 ab

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Aim: How do we find the derivative by limit process? Do Now: Find the slope of the secant line in terms of x and h. y x (x, f(x)) (x + h, f(x + h)) h.

Aim: How do we find the derivative by limit process? Do Now: Find the slope of the secant line in terms of x and h. y x (x, f(x)) (x + h, f(x + h)) h.

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