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# Bit of C3 (differentiating lns) watch

1. I'm trying to show the minimum value of y = x² -lnx is 1/2(1+ln2)

I think you have to differentiate so I get 2x - 1/x

To find stationary points dy/dx = 0 so 2x - 1/x = 0

A bit of fiddling gives x = ±root1/2

Assuming this bit is right, where do I go from here? I'm guessing I should differentiate again and find the maximum/minimum points, but doing so wont have anything to do with ln2 in it...

Any ideas TSR?
2. No, imtired. We know that log(x) is only real for x>0, so we don't need to differentiate again.

OP: Substitute your value of x back in to find y. A little bit of fiddling gives the ln(2).
3. (Original post by Kolya)
No, imtired. We know that log(x) is only real for x>0, so we don't need to differentiate again.

OP: Substitute your value of x back in to find y. A little bit of fiddling gives the ln(2).
Plugging in root1/2 gives y = 1/2 - ln(root1/2) (the other value of x is not needed because you cant get the ln of a minus number)

So y = 1/2 - ln1 - ln(root2)

This gives 1/2 + ln(root2) and not ln2...
where am I going wrong?
4. (Original post by ChrisKing)
Plugging in root1/2 gives y = 1/2 - ln(root1/2) (the other value of x is not needed because you cant get the ln of a minus number)

So y = 1/2 - ln1 - ln(root2)

This gives 1/2 + ln(root2) and not ln2...
where am I going wrong?

Laws of logs anyone?
5. (Original post by sonofdot)

Laws of logs anyone?
Oh dear, I love the way I forget my core 1 and 2 stuff

Thank you!

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