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, $y'=0$.

$1-0.08x=0$

$-0.08x=-1$

$x=\dfrac{-1}{-0.08}$

$x=12.5$

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.