Question

I'm a newbie here! Please help me.

Find two real numbers whose sum is 24 and whose product is a minimum.

Answer 1

Sure ^_^
Let's let those two numbers be x and y for now... ok?

Answer 2

sure

Answer 3

Given: x + y = 24

Minimize: xy

Or xy = x(24 - x)...substituting 24 - x for y.

So we want to minimize x(24 - x) = 24x - x^2

Take its derivative (to find minimum), you get 24 - 2x

Set equal to zero to find critical points... 24 - 2x = 0
x = 12...is a critical point. However x = 12 is a rel max, so x = 12 and hence y = 12 will be the maximum values of x and y that will maximize xy or a product of 144.

This function has no minimum.

Answer 4

Thank you so much for helping me! :) @Easyaspi314

Answer 5

welcome. I would think that you would be asked to find values of x and y that will maximize xy, given that x+y = 24.

Answer 6

OK :) @Easyaspi314