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