Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? Give reasons for your answer.

$f(x)=x^{\frac{4}{9}}$;$[-1,5]$

Choose the correct answer below.

A$.$ Yes, $f(x)$ is continuous for every point of $-1,5$ and differentiable for every point in $(-1,5).$

B$.$ Yes, $f(x)$ is continuous for every point of $(-1,5)$ and differentiable for every point in $-1,5.$

C$.$ No$,f(x)$ is continuous for every point of $-1,5$ but is not differentiable for every point in $(-1,5).$

D$.$ No$,f(x)$ is differentiable for every point in $(-1,5)$ but is not continuous for every point of $-1,5.$