Can the Mean value theorem be applied ? What is the value of C? 1. Determine if the Mean Value Theorem can be applied to the following function on the given closed interval. If so, find all possible values of $ c $:\[ f(x) = 3 + \sqrt{x} \]on $[0, 4]$.\[ f(c) = \frac{f(b) - f(a)}{b - a} \]Mean Value Theorem\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]\[ f(b) = y_2 \]\[ f(a) = y_1 \]Graph Explanation:The graph sketched represents the function $ f(x) = 3 + \sqrt{x} $ on a coordinate plane. The x-axis is labeled from 0 to 5, and the y-axis is labeled from 0 to 5. A curve, representing the square root function shifted up by 3 units, starts at point (0, 3) and increases to point (3, 5). The curve appears to follow the shape anticipated for a square root function, indicating it is continuous and differentiable on the interval [0, 4].

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Calculus

Can the Mean value theorem be applied ? What is the value of C?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Can the Mean value theorem be applied ? What is the value of C?

1. Determine if the Mean Value Theorem can be applied to the following function on the given closed interval. If so, find all possible values of $ c $:

\[ f(x) = 3 + \sqrt{x} \]

on $[0, 4]$.

\[ f(c) = \frac{f(b) - f(a)}{b - a} \]

Mean Value Theorem

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

\[ f(b) = y_2 \]
\[ f(a) = y_1 \]

Graph Explanation:
The graph sketched represents the function $ f(x) = 3 + \sqrt{x} $ on a coordinate plane. The x-axis is labeled from 0 to 5, and the y-axis is labeled from 0 to 5. A curve, representing the square root function shifted up by 3 units, starts at point (0, 3) and increases to point (3, 5). The curve appears to follow the shape anticipated for a square root function, indicating it is continuous and differentiable on the interval [0, 4].

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