Q. 49 - 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=1.2

Step 1. Given information

Step 2. Explanation

From graph,

$$\begin{gathered} f\left(0\right)=0 \\ f\left(2\right)=4 \end{gathered}$$

From MVT,

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

$f\text{'}\left(c\right)=\frac{f\left(2\right)-f\left(0\right)}{2-0}$

$f\text{'}\left(c\right)=\frac{4-1}{2-0}$

$f\text{'}\left(c\right)=\frac{3}{2}$

Since, $c\in (0,2)$, c=1.2