Checkpoint 2

1. For the function ${\displaystyle h\text{(}t\text{)}=-t^3+12t}$, find the numbers ${\displaystyle t}$ for which ${\displaystyle h\text{'}\text{(}t\text{)}=0.}$

2. Confirm that the second derivative identifies which of these inputs makes ${\displaystyle h\text{(}t\text{)}}$ a local maximum and which makes ${\displaystyle h\text{(}t\text{)}}$ a local minimum.