Question

Find all the values of x for which the function is differentiable.

f(x)= (x^3-8)/(x^2-4x-5)

Answer 1

A function is differentiable when The function is continuous.
\[\frac{x^3-2^3}{x^2 - 4x -5}\]Just check x for which denominator is equal to zero exclude those values and you have a differentiable function in Real Domain.

Answer 2

\[x^2 - 4x - 5 \neq 0 \]

Answer 3

It would be differentiable at all real numbers except 5 and -1?

Answer 4

Yea, you got that right.