The height # h# in feet of a baseball seconds after being hit upward is given by #h(t) = - 16t^2 + 80t + 3#. What is the maximum height that the baseball reaches, and when does this occur?

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Answer 1 · 2017-12-06T05:39:30

103

2.5 s

#sf(h=-16t^2+80t+3)#

To find the maximum we put the 1st derivative equal to zero:

#sf((dh)/(dt)=-32t+80)#

This equals zero at the maximum:

#sf(-32t+80=0)#

#sf(32t=80)#

#sf(t=80/32=2.5color(white)(x)s)#

This is the time taken to reach the maximum height. To find the height:

#sf(h=(-16xx2.5^2)+(80xx2.5)+3=103)# graph{-16x^2+80x+3 [-291.7, 291.7, -145.8, 145.8]}