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What is the maximum height of of Anna's golf ball? The equation is y=x−0.04x2.

User Ilijaluve
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1 Answer

4 votes

Given:

The height of a golf ball is represented by the equation:


y=x-0.04x^2

To find:

The maximum height of of Anna's golf ball.

Solution:

We have,


y=x-0.04x^2

Differentiate with respect to x.


y'=1-0.04(2x)


y'=1-0.08x

For critical values,
y'=0.


1-0.08x=0


-0.08x=-1


x=(-1)/(-0.08)


x=12.5

Differentiate y' with respect to x.


y''=(0)-0.08(1)


y''=-0.08

Since double derivative is negative, the function is maximum at
x=12.5.

Substitute
x=12.5 in the given equation to get the maximum height.


y=(12.5)-0.04(12.5)^2


y=12.5-0.04(156.25)


y=12.5-6.25


y=6.25

Therefore, the maximum height of of Anna's golf ball is 6.25 units.

User Selina
by
8.7k points
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