Mark M. answered • 10/27/21

Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.

Let x = larger number and y = smaller number

We are given that x - y = 96. So, y = x - 96.

Minimize P = xy = x(x - 96) = x^{2} - 96x

dP/dx = 2x - 96

dP/dx = 0 when x = 48

When x < 48, dP/dx < 0. So, P is decreasing

When x > 48, dP/dx > 0. So, P is increasing.

P is minimized when x = 48and y = -48

Mark M.

10/28/21

James D.

the larger number is 48, so it cannot be that the smaller number is -4910/28/21