Let $f$ be a function continuous on the closed interval $[-2, 5]$ and differentiable on the open interval $(-2, 5)$. If $f(-2) = 1$ and $f(5) = 22$, which of the following statements must be true?

Question

Accepted Answer

A. There exists a value $c$ in $(-2, 5)$ such that $f'(c) = 3$.

Answer

There exists a value $c$ in $(-2, 5)$ such that $f'(c) = 3$.

Answer

There exists a value $c$ in $(-2, 5)$ such that $f'(c) = 0$.

Answer

The function $f$ must have a relative extremum on the open interval $(-2, 5)$.

Answer

There exists a value $c$ in $(-2, 5)$ such that $f(c) = 0$.

Let $f$ be a function continuous on the closed interval $[-2, 5]$ and differentiable on the open interval $(-2, 5)$ . If $f(-2) = 1$ and $f(5) = 22$ , which of the following statements must be true?

Explanation

Core Concept

Correct Answer

More Unit 5: Analytical Applications of Differentiation practice questions

Let fff be a function continuous on the closed interval [−2,5][-2, 5][−2,5] and differentiable on the open interval (−2,5)(-2, 5)(−2,5). If f(−2)=1f(-2) = 1f(−2)=1 and f(5)=22f(5) = 22f(5)=22, which of the following statements must be true?

Explanation

Core Concept

Correct Answer

More Unit 5: Analytical Applications of Differentiation practice questions

Let $f$ be a function continuous on the closed interval $[-2, 5]$ and differentiable on the open interval $(-2, 5)$ . If $f(-2) = 1$ and $f(5) = 22$ , which of the following statements must be true?