Question

consider the function f given below
f(x) = \frac{x^2 - 9}{x + 3}
a) for what x-value(s) is this function not differentiable?
b) find f(5)
a) f(x) is not differentiable at x = \square (use a comma to separate answers as needed.)
b) f(5) = \square.

Explanation:

Step1: Simplify the function

Factor numerator: $x^2 - 9 = (x-3)(x+3)$. Cancel $x+3$ (for $x
eq -3$): $f(x) = x - 3$ when $x
eq -3$.

Step2: Check differentiability

$f(x)$ is undefined at $x = -3$, so not differentiable there.

Step3: Find derivative of simplified function

$f'(x) = 1$ for $x
eq -3$.

Step4: Compute $f'(5)$

Substitute $x=5$ into $f'(x)$: $f'(5) = 1$.

Answer:

a) $-3$
b) $1$