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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.

What is the maximum height the dolphin can jump?

  • math -

    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.

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