Given:
The height of a golf ball is represented by the equation:
![y=x-0.04x^2](https://tex.z-dn.net/?f=y%3Dx-0.04x%5E2)
To find:
The maximum height of of Anna's golf ball.
Solution:
We have,
![y=x-0.04x^2](https://tex.z-dn.net/?f=y%3Dx-0.04x%5E2)
Differentiate with respect to x.
![y'=1-0.04(2x)](https://tex.z-dn.net/?f=y%27%3D1-0.04%282x%29)
![y'=1-0.08x](https://tex.z-dn.net/?f=y%27%3D1-0.08x)
For critical values,
.
![1-0.08x=0](https://tex.z-dn.net/?f=1-0.08x%3D0)
![-0.08x=-1](https://tex.z-dn.net/?f=-0.08x%3D-1)
![x=\dfrac{-1}{-0.08}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-1%7D%7B-0.08%7D)
![x=12.5](https://tex.z-dn.net/?f=x%3D12.5)
Differentiate y' with respect to x.
![y''=(0)-0.08(1)](https://tex.z-dn.net/?f=y%27%27%3D%280%29-0.08%281%29)
![y''=-0.08](https://tex.z-dn.net/?f=y%27%27%3D-0.08)
Since double derivative is negative, the function is maximum at
.
Substitute
in the given equation to get the maximum height.
![y=(12.5)-0.04(12.5)^2](https://tex.z-dn.net/?f=y%3D%2812.5%29-0.04%2812.5%29%5E2)
![y=12.5-0.04(156.25)](https://tex.z-dn.net/?f=y%3D12.5-0.04%28156.25%29)
![y=12.5-6.25](https://tex.z-dn.net/?f=y%3D12.5-6.25)
![y=6.25](https://tex.z-dn.net/?f=y%3D6.25)
Therefore, the maximum height of of Anna's golf ball is 6.25 units.
Other ways are m<1, YFP and m<F.
The angle is an acute angle because it is less than a right angle (less than 90 degrees).
D. 90 im pretty sure its this. hope this helped :)
Question Two is D. $14.80