17. A bottlenose dolphin jumps out of the water. The path the dolphin Travels can be
modeled by h = -0.2d2 + 2d, where h represents the height of the dolphin and d
represents horizontal distance.
a. What is the maximum height the dolphin reaches?
b. How far did the dolphin jump?

Respuesta :

Answer:

a. 5 units

b. 5 units

Step-by-step explanation:

Given:

The path the dolphin Travels can be  modelled by [tex]h = -0.2d^2 + 2d[/tex] where  h represents the height of the dolphin and d  represents horizontal distance.

To find: maximum height that the dolphin reaches and the distance covered by dolphin

Solution:

[tex]h = -0.2d^2 + 2d[/tex]

Differentiate with respect to [tex]d[/tex]

[tex]\frac{\mathrm{d} h}{\mathrm{d} d}=-0.4d+2[/tex]

To find the critical point, put [tex]\frac{\mathrm{d} h}{\mathrm{d} d}=0[/tex]

[tex]d=\frac{2}{0.4}\\=\frac{20}{4}\\=5 \,\,units[/tex]

Differentiate [tex]\frac{\mathrm{d} h}{\mathrm{d} d}[/tex] again with respect to [tex]d[/tex]

[tex]\frac{\mathrm{d^2} h}{\mathrm{d} d^2}=-0.4<0[/tex]

So, [tex]d=5[/tex] is a point of maxima

[tex]h(5) = -0.2(5)^2 + 2(5)\\=-0.2(25)+10\\=-5+10\\=5\,\,units[/tex]

a. 5 units

b. 5 units

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