Consider the function $\mathrm{f}$ given below.
\[
f(x)=\frac{x^{2}-64}{x-8}
\]
a) For what $x$-values(s) is this function not differentiable?
b) Find $f^{\prime}(-9)$.

Answer

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Answer

Final Answer: The function is not differentiable at $x=\boxed{8}$.

Steps

Step 1 ：Consider the function $f(x)=\frac{x^{2}-64}{x-8}$.

Step 2 ：We need to find the x-values where the denominator of the function, which is $x-8$, is zero.

Step 3 ：Solving the equation $x-8=0$, we find that $x=8$.

Step 4 ：Therefore, the function is not differentiable at $x=8$.

Step 5 ：Final Answer: The function is not differentiable at $x=\boxed{8}$.