- #1
benmuskler
- 6
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Hello everyone! I'm stuck on a small detail in a math task, and would really appreciate some help!
Determine all local extreme points and possible max/min values for the function f(x) = x*lnx+(x*lnx)^2 where 0<x≤1/2
The first thing I did was to differentiate f, giving me f'(x)=(lnx+1)(1+2x*lnx)
Then, in order to find extreme points, I tried to solve f'(x)=0
So, either (lnx+1)=0 [itex]\rightarrow[/itex] x=1/e
or (1+2x*lnx) = 0 [itex]\rightarrow[/itex] x*lnx = -1/2
And this is where I get stuck. How do I solve that equation?
Homework Statement
Determine all local extreme points and possible max/min values for the function f(x) = x*lnx+(x*lnx)^2 where 0<x≤1/2
Homework Equations
The Attempt at a Solution
The first thing I did was to differentiate f, giving me f'(x)=(lnx+1)(1+2x*lnx)
Then, in order to find extreme points, I tried to solve f'(x)=0
So, either (lnx+1)=0 [itex]\rightarrow[/itex] x=1/e
or (1+2x*lnx) = 0 [itex]\rightarrow[/itex] x*lnx = -1/2
And this is where I get stuck. How do I solve that equation?