Question

Does the MVT apply? Explain why or why not. y=x^2/4x + 4 ; [-6, -2]

Answer 1

Hello!

$\large\boxed{\text{Yes, it does.}}$

In order to use the MVT, the function must be continuous over the given interval.

$y = \frac{x^{2} }{4x}+4$

Simplifies to:

$y = \frac{x}{4} + 4$

This is a linear equation that is continuous on the interval (-∞, ∞), which  means that it would also be continuous on the interval [-6, -2]. The MVT would apply to this function.