a bootlenose dolphin jumps out of the water. the path the dolphin travels can be modeled by h=-0.2d^2+2d, where h represents the height of the dolphin in feet and d represents the horizontal distance.

Question

What is the maximum height the dolphin can jump?

Answer 1

h(d)=-0.2d^2+2d
To find the maximum (or minimum), we find the derivative with respect to d and equate to zero.

h'(d) = -0.4d+2 = 0
=>
d = 2/0.4 = 5 ft.

Check that this is the maximum:
method 1:
a parabola with a negative coefficient has only one maximum and no minimum.
method 2:
check sign of h"(d) where d=5'
h"(d) = -0.4 <0 => maximum.