Simple application of Derivitives problem

[Leonidas]

Find two positive numbers that satisfy the given requirements.


The Product is 192 and the sum is a minimum.


I said that x*y=192 and y=192/x and that dy/dx= -192/x^2

I thought that we were supposed to set the derivative equal to zero in order to find the local extrema... however -192/x^2 does not equal 0...right?

I'm dazed and confused... can someone please help?

 

[Pyrrhus]

You should have done

$$xy = 192$$

$$y = \frac{192}{x}$$

$$x + y = (number)$$

Minimize this:
$$x + \frac{192}{x} = (number)$$

 

[Leonidas]

oh.

...

1. That was really fast... thanks.

2. I should have seen that.

3.