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Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function A = 24x-x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area?

Respuesta :

We are given

[tex]A=24x-x^2[/tex]

where

x is width of rectangle

A is area of rectangle

Since, we have to maximize it

so, we will find it's derivative

and then we can set it to 0

and then we can solve for x

[tex]A'=24\times 1-2x[/tex]

[tex]A'=24-2x[/tex]

now, we can set it to 0

and then we can solve for x

[tex]A'=24-2x=0[/tex]

[tex]x=12[/tex]

So, width is 12  feet

Maximum area:

we can plug x=12

[tex]A=24(12)-(12)^2[/tex]

[tex]A=144ft^2[/tex]

So, the maximum area is

[tex]=144ft^2[/tex]................Answer

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