Yefim S. answered • 6d

Math Tutor with Experience

Let dementions of frame x and y. Then dimentions of picture is (x - 4) and (y - 3) and area A = (x - 4)(y - 3) =

xy - 3x - 4y + 12; A = 132 - 3x - 4y. Now xy = 120; y = 120/x and we get A(x) = 132 - 3x - 480/x;

A'(x) = - 3 + 480/x^{2} = 0; x^{2} = 160; x = ±4√10. We have 2 critical numbers.

Now A''(x) = - 960/x^{3}; A''(4√10) = - 960/(4√10)^{3} < 0 and by 2nd derivative test we have at x = 4√10 maximum

y = 120/(4√10) = 3√10

Answer: for x = 4√10 inch and y = 3√10 inch