(c) The derivative of a function at a given point is the slope of the tangent line at that point. So, if you can’t draw a tangent line, there’s no derivative.
From the graph, we can determine the values of x that f'(x) is undefined to be:
![-3,\text{ -1, 3, 5}](https://img.qammunity.org/2023/formulas/mathematics/college/ih3f1jem1uq2byyfdn09cjjik1smbqursq.png)
Answer: -3, -1, 3, 5
(d) The derivative of a function is zero when there is a horizontal tangent at that point.
From the graph, we can determine the values of x where f'(x) is zero to be:
![0,\text{ 2}](https://img.qammunity.org/2023/formulas/mathematics/college/ebyqunc66920rdb80h7ul36kip6uovwuer.png)
Answer: 0, 2