can you please do c and d, can you please provide explanations B1. (a) State the Mean Value Theorem for a function f that is continuous on [a, b] anddifferentiable on (a, b).(b) Verify the Mean Value Theorem on [1,3] when f(x) = 5x² – x³.(c) A function f is defined byf(x) = {sin² xwhen x < 0,cos x when x ≥ 0.Does the Mean Value Theorem apply to f on [-, π]?(d) By applying the Mean Value Theorem to a function f on a suitable interval, showthatƒ(x) = f(x) + ƒ'(c)(x − xo),where c lies between co and x.(e) Suppose that f(x) = g(x) = 0, and g'(x) ‡ 0. Use the results of part (d) toshow thatlimx-xo=f'(xo)g'(xo)log(1+log x)(f) Use the result of part (e) to evaluate limx→1 (log(2x²-1)

b) Verify the Mean Value Theorem on [1,3] when ƒ(x) = 5x² – x³. =) A function f is defined by f(x) = { sin²x 1 - cos x when x < 0, when x ≥ 0. Does the Mean Value Theorem apply to ƒ on [-, π]? d) By applying the Mean Value Theorem to a function ƒ on a suitable interval, show that ƒ(x) = f(x) + ƒ'(c)(x − xo), - where c lies between co and x. e) Suppose that f(xo) = g(xo) = 0, and g'(x) ‡ 0. Use the results of part (d) to show that ƒ(x)` lim x+xo (g(x) = f'(xo) g'(x) log(1+log x) =) Use the result of part (e) to evaluate limx→1 (log(2x²-1)

b) Verify the Mean Value Theorem on [1,3] when ƒ(x) = 5x² – x³. =) A function f is defined by f(x) = { sin²x 1 - cos x when x < 0, when x ≥ 0. Does the Mean Value Theorem apply to ƒ on [-, π]? d) By applying the Mean Value Theorem to a function ƒ on a suitable interval, show that ƒ(x) = f(x) + ƒ'(c)(x − xo), - where c lies between co and x. e) Suppose that f(xo) = g(xo) = 0, and g'(x) ‡ 0. Use the results of part (d) to show that ƒ(x)` lim x+xo (g(x) = f'(xo) g'(x) log(1+log x) =) Use the result of part (e) to evaluate limx→1 (log(2x²-1)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 2E

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