IVT, MVT, and Rolle's Theorem Question 3

Let $f$ be a function that is continuous on the closed interval $[3,10]$ with $f(3)=0$ and $f(10)=10$ . Which of the following is guaranteed by the Intermediate Value Theorem?

f(x)=6

has at least one solution in the open interval

(3,10)

f(7)=5

f

attains a maximum on the open interval

(3,10)

f'(x)=\dfrac{10}{7}

has at least one solution in the open interval

(3,10)

Approach

The Intermediate Value Theorem gurantees that there will be a point with value

f(c)

where

0\lt f(c)\lt 10

The last answer choice is also guranteed, but through the Mean Value Theorem and only if the function is also differentiable on the closed interval.