find x-value where U (x) = 72 - (4 + x)^2 - (4-rx)^2 is max

[thelazyman]

Hi have difficulty with the following quadratic equation, dont really know how to simplify the equation.

U (x) = 72 - (4 + x)^2 - (4-rx)^2

where r is a constant. Find the value of x for which U (x) attains its largest value.

Dont really now where to start in thsi equation. Someone please help.

Thank you

 

[galactus]

Find the derivative of U(x). Set to 0 and solve for x. It'll be in terms of r.

A way to check if this is, indeed, a maximum is to find the second derivative. If it's negative, it's a relative max.