최대 1 분 소요

# Concepts

## The Mean Value Theorem

Lef $f$ be a function that satisfies the following hypotheses:

1. $f$ is continuous on the closed interval $[a, b]$.
2. $f$ is differentiable on the open interval $(a, b)$.

Then there is a number $c$ in $(a, b)$ such that

$f^{'}(c) = \frac{f(b) - f(a)}{b - a}$

or, equivalently,

$f(b) - f(a) = f^{'}(c)(b - a)$

# Questions

Consider the following function and closed interval.

$f(x) = x^{3} - 3x + 4, [-2, 2]$

## Question 1

Find $\frac{f(b) - f(a)}{b - a}$ for $[a, b] = [-2, 2]$. (If an answer does not exist, enter DNE.)

$\frac{f(b) - f(a)}{b - a} = ?$

## Question 2

If the mean value theorem can be applied, find all values of $c$ that satisfy the conclusion of the mean value theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).

$c = ?$