Use a graph of the function to find the derivative of the function at the given point, if it exists.
-$f(x)=\left\{\begin{array}{cl}
\frac{(x-3)(x-5)}{x-3} & x \neq 3 \
-2 & x=3
\end{array} \quad \text { at } x=3\right.$
A) 0
B) 1
C) Does not exist
D) $- 1$

Question

Quizplus · Accepted Answer

The function simplifies to $f(x) = x - 5$ for $x \neq 3$. The derivative of $f(x) = x - 5$ is 1, and since the function is continuous at $x = 3$, the derivative at $x = 3$ is also 1.

Use a Graph of the Function to Find the Derivative f(x)={(x−3)(x−5)x−3x≠3−2x=3 at x=3f(x)=\left\{\begin{array}{cl}\frac{(x-3)(x-5)}{x-3} & x \neq 3 \\-2 & x=3\end{array} \quad \text { at } x=3\right.f(x)={x−3(x−3)(x−5)​−2​x=3x=3​ at x=3

Use a Graph of the Function to Find the Derivative $f(x)=\left\{\begin{array}{cl}\frac{(x-3)(x-5)}{x-3} & x \neq 3 \\-2 & x=3\end{array} \quad \text { at } x=3\right.$