Answer
The slope of the secant line as we approach to $x=3$ from the left is 0. The slope of the secant line as we approach to $x=3$ from the right is
$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{2-1}{5-3}=\frac{1}{2}$.
As the left-hand derivative and the right-hand derivative does not coincide at $x=3$, the derivative at $x=3$ does not exist for this function. That is, $f'(3) $ does not exist.
Work Step by Step
See the answer above.
