13. a catapult launches a boulder wint an upward velocity of 122 feet per second the height of the boulder (h) in feet after t seconds is given by the function h(t)=-16t^2+122t+10. how long does it take the boulder to reach maximum height? what is the boulders maximum height? round to the nearest hundredth if necessary.

For this case we have the following expression:
 h (t) = - 16t ^ 2 + 122t + 10
 We look for the maximum of the function, for this, we derive:
 h '(t) = - 32t + 122
 We match zero:
 -32t + 122 = 0
 We cleared t:
 t = 122/32
 t = 3.8125 s
 Then, the maximum height will be:
 h (3.8125) = - 16 * (3.2185) ^ 2 + 122 * (3.2185) +10
 h (3.8125) = 236.92 feet
 
 It takes the boulder to reach maximum height about:
 t = 3.8125 s
 the boulders maximum height is:
 236.92 feet