Answer
(a) The function has a local maximum at the point $x=2$. The function is differentiable at the point $x=2$.
(b) The function has a local maximum at the point $x=2$. The function is continuous. The function is not differentiable at the point $x=2$.
(c) The function has a local maximum at the point $x=2$. The function is not continuous at the point $x=2$.
Work Step by Step
(a) The function has a local maximum at the point $x=2$. Also, $f'(2)=0$, so $f'(2)$ exists. Therefore, the function is differentiable at the point $x=2$.
(b) The function has a local maximum at the point $x=2$. The function is continuous. However, $f'(2)$ does not exist. Therefore, the function is not differentiable at the point $x=2$.
(c) The function has a local maximum at the point $x=2$. The function is not continuous at the point $x=2$.
