Question

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

Answer 1

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.