Question

Find the point of diminishing returns left parenthesis x comma y right parenthesis(x,y) for the function​ R(x), where​ R(x) represents revenue​ (in thousands of​ dollars) and x represents the amount spent on advertising​ (in thousands of​ dollars).

Answer 1

To do this problem, I'm pretty sure you just have to find the maximum:

f(x)=11000-x^3+36x^2+600x
f'(x)=-3x^2+72x+600

Set f'(x) to be 0

0=-3x^2+72x+600
0=x^2-24x-200

The only positive x value is 30.54

Now we plug this into f(x)

f(30.54)=11000-30.54^3+36(30.54)^2+600(30.54)=34416.5
Thus we get (30.54,34416.5)

Of course, I'm not as confident about this one as the other ones, however, so you may need to double check my work!