For f(x) =does the Mean Value Theorem apply on the interval [0, 2] and why?(I-1)O The Mean Value Theorem applies because f(x) is differentiable on the open interval (0, 2).O The Mean Value Theorem applies because f(x) is continuous on [0, 2].O The Mean Value Theorem does not apply because f(x) is not continuous on the closed interval [0, 2].O The Mean Value Theorem applies because, f(x) is differentiable on the closed interval [0, 2].

Mean value theorem: f(x)=x2+x-2x-1 =x2+2x-x-2x-1 =x(x+2)-1(x+2)x-1 =(x+2)(x-1)(x-1)…

Answered: lue Theorem apply on th es because f(x)…

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lue Theorem apply on th es because f(x) is differe es because f(x) is contin not apply because f(x) is

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

For f(x) =
does the Mean Value Theorem apply on the interval [0, 2] and why?
(I-1)
O The Mean Value Theorem applies because f(x) is differentiable on the open interval (0, 2).
O The Mean Value Theorem applies because f(x) is continuous on [0, 2].
O The Mean Value Theorem does not apply because f(x) is not continuous on the closed interval [0, 2].
O The Mean Value Theorem applies because, f(x) is differentiable on the closed interval [0, 2].

Expert Solution

Step 1

Mean value theorem:

$f (x) = \frac{x^{2} + x - 2}{x - 1} = \frac{x^{2} + 2 x - x - 2}{x - 1} = \frac{x (x + 2) - 1 (x + 2)}{x - 1} = \frac{(x + 2) (x - 1)}{(x - 1)} = (x + 2)$

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