Q. 50 - 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

Step 1. Given information

Step 2. Explanation

From the graph,

$$\begin{gathered} f(-1)=1 \\ f\left(3\right)=8 \end{gathered}$$

From MVT,

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

$f\text{'}\left(c\right)=\frac{f(-1)-f\left(3\right)}{-1-3}$

$f\text{'}\left(c\right)=\frac{8-1}{-1-3}$

$f\text{'}\left(c\right)=-\frac{7}{4}$

 c=0