# Maximum value homework

1. Aug 13, 2008

### dan_fmx

Hi im new on the forums here. I am having troube with my maths assignment. It says to find the maximum value of y= kx³ . ln(1/x) where k is a positive constant. I am also told to find the value of x, in terms of e. I am really struggling and any help would be appreciated.

Dan

2. Aug 13, 2008

### Defennder

Re: Maximum

What do you know about calculus you can use to find the max value of a function?

3. Aug 13, 2008

### CompuChip

Re: Maximum

If this is an assignment, I'm sure it relates to what you are currently covering. Does that, by any chance, have something to do with derivatives? Can you (perhaps looking back in your notes) tell us how, in general, you can find the x-coordinate where the function y(x) takes its maximum?

4. Aug 13, 2008

### dan_fmx

Re: Maximum

The maximum will be found when the gradient function = 0. I found the gradient function using the product rule as y'=-x²+3x².Ln(1/x). Then when 0=-x²+3x².Ln(1/x) x= 0.7165. How ever it says in terms of e and this is where i get really stuck. I am drawing a blank on this one

5. Aug 13, 2008

### HallsofIvy

Staff Emeritus
Re: Maximum

Okay, -x2+ 3x2ln(1/x)= x2(3 ln(1/x)- 1)= 0 so one possible solution is x= 0. The other is given by 3 ln(1/x)= 1 or ln(1/x)= 1/3. Surely you can find x without resorting to a calculator? If ln(x)= a, the x= ea by definition.

Last edited: Aug 14, 2008
6. Aug 13, 2008

### dan_fmx

Re: Maximum

Wow it all became so clear, thanks so much for all the help everyone. I found the maximum x value to be x=1/(e^(1/3)). Thanks everyone for helping