17. Given_{}, on_{}

**(a) ****Find the critical numbers of the first-order**

**Solution: **We compute the first derivative, and set it equal to zero

_{}

Hence, the critical points are_{}and_{}.

**(b) ****Find the intervals of increase and decrease. Show work that supports conclusion**

**Solution: **The derivative is equal to

_{}

- The function is increasing if
_{}

_{}

- The function is decreasing if
_{}

_{}

**(c) ****Give the coordinates of the local maximum, if any**

**Solution: **We find the second derivative

_{}

_{}. This means that_{} is a local maximum

Therefore, the coordinates of the local maximum is (2, 37).

**(d) ****Give the coordinates of the local minimum, if any**

**Solution: **Similarly

_{}. This means that_{} is a local minimum.

Therefore, the coordinates of the local maximum is (6, 5).

**(e) ****Find the intervals on which f(x) is concave up and the intervals on which it is concave down. Show the work. Find the coordinates of the inflection point, if there is any**

**Solution: **We already calculated the second derivative

_{}

_{}