3. The following relate to Rolle's Theorem, which is stated as follows. If function f: [a, b] → R is continuous at every point in its domain, differentiable every point on the interval (a, b), and satisfies the relation f(a) = f(b), then there must be a point o on the interval (a, b) such that f'(x) = 0. A. Rolle's Theorem is just a special case of the Mean Value Theorem. Explain. B. Rolle's Theorem does not apply to the function g: [-2, 2] → R defined by g(x) = |x|. Explain. C. Rolle's Theorem does apply to the function g: [-2, 0]→ R defined by g(x) = x³ + x² - 2x. Explain.
3. The following relate to Rolle's Theorem, which is stated as follows. If function f: [a, b] → R is continuous at every point in its domain, differentiable every point on the interval (a, b), and satisfies the relation f(a) = f(b), then there must be a point o on the interval (a, b) such that f'(x) = 0. A. Rolle's Theorem is just a special case of the Mean Value Theorem. Explain. B. Rolle's Theorem does not apply to the function g: [-2, 2] → R defined by g(x) = |x|. Explain. C. Rolle's Theorem does apply to the function g: [-2, 0]→ R defined by g(x) = x³ + x² - 2x. Explain.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.1: Inverse Functions
Problem 56E
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