find maximum height of y=128x-16x^2

Question

college algebra

Answer 1

y = 128x - 16x²

 

To find the maximum you want to differentiate the equation.

So,

dy/dx = 128 - 16*2x = 128 - 32x

 

You will then find the maximums and minimums when you put dy/dx = 0

 

So, 128 - 32x = 0

- 32x = - 128

x = (- 128)/(- 32)

x = 4

 

And by subtituting this value (x = 4) into the original equation we can find the value that y has when x = 4

 

So, y = 128x - 16x² = 128*4 - 16*(4)² = 512 - 256 = 256

 

So the equation is at a max at (4, 256)

 

[if it's required you can confirm that it is a max point by doing a table of signs. i.e. looking at whether dy/dx is bigger or smaller than zero before and after x = 4]