Q. 52 - Calculus

Question

For each graph of f in Exercises 49–52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

Step-by-Step Solution

Answer

The graph satisfies the mean value theorem and c=0.5, 1, 3.5

Step 1. Given information

Step 2. Explanation

From graph,

$$\begin{gathered} f\left(0\right)=0.1 \\ f\left(4\right)=1 \end{gathered}$$

From MVT, 

$f\text{'}\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

$f\text{'}\left(c\right)=\frac{f\left(4\right)-f\left(0\right)}{4-0}$

$f\text{'}\left(c\right)=\frac{1-0.1}{4}$

$f\text{'}\left(c\right)=\frac{0.9}{4}$