Question

Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

$f\left(x\right)=x^2+\frac{1}{x},[a,b]=[-3,2]$

Short answer

f(x) isn't continuous and differentiable on the given interval.

Step-by-step solution

Step 1. Given information

$f\left(x\right)=x^2+\frac{1}{x}$for a=-2 and b=3

Step 2. Proving Mean Value Theorem  

Since,

$0\in [-3,2]$

$f\left(0\right)=0^2+\frac{1}{0}$

f(0)=undefined