Hello!
[tex]\large\boxed{\text{Yes, it does.}}[/tex]
In order to use the MVT, the function must be continuous over the given interval.
[tex]y = \frac{x^{2} }{4x}+4[/tex]
Simplifies to:
[tex]y = \frac{x}{4} + 4[/tex]
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.
