How to Find Critical Points of f(x) = xln(x)

jtulloss
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I need help finding the critical points of this equation:

f(x) = xln(x)

I found f'(x) to be ln(x)+x, but I don't know how to solve for x when setting f'(x) to 0 to find the critical points. I know I can find the zeros of f'(x) graphically on a calculator, but I need to know how to do it algebraically.

Thanks.
 
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jtulloss said:
I need help finding the critical points of this equation:

f(x) = xln(x)

I found f'(x) to be ln(x)+x,
It's not lnx + x.
 
Ah man, I can't believe I overlooked that. I've been doing that a lot lately with studying for exams and all. I got it now.

Thanks
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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