Apply the Mean Value Theorem to the following function h ( x ) h(x) on the interval [ m , n ] [m, n] and show that the number p p guaranteed by the theorem is the midpoint of the interval. h ( x ) = M x 2 + N x + P h(x)=Mx^2+Nx+P , where M M , N N , and, P P are real numbers and M ≠ 0 M≠0

Table of contents

4. Applications of Derivatives

Differentials

4. Applications of Derivatives

Differentials: Study with Video Lessons, Practice Problems & Examples

9PRACTICE PROBLEM

ANSWERS OPTIONS

The number $p$ guaranteed by the Mean Value Theorem is the midpoint of the interval $[m, n]$ , where $p = n - m$ .

The number $p$ guaranteed by the Mean Value Theorem is the midpoint of the interval $[m, n]$ , where $p = \frac{n - m}{2}$ .

The number $p$ guaranteed by the Mean Value Theorem is the midpoint of the interval $[m, n]$ , where $p = n + m$ .

The number $p$ guaranteed by the Mean Value Theorem is the midpoint of the interval $[m, n]$ , where $p=\frac{n+m}{2}$ .