MHB Determine the location and nature of turning point

[markosheehan]

whats the turning point of (1-lnx)², x>2 is it a minimum or maximum. can someone help me

 

[Evgeny.Makarov]

Re: calculus

We have $$(1-\ln x)^2\ge0$$ and, moreover, $(1-\ln x)^2=0\iff \ln x=1$. Can you find the solution of $\ln x =1$?

 

[markosheehan]

how do you get the derivative of it

 

[Evgeny.Makarov]

As for any composition of functions. The outer function if $f(x)=x^2$, so first you differentiate $x^2$, and the result is $2x$. Now our whole function is not $f(x)$, but $f(1-\ln x)$. Therefore you replace $x$ in $2x$ with $1-\ln x$ to get $2(1-\ln x)$. To finish, you need to multiply this by the derivative of $1-\ln x$.

I recommend reviewing the chain rule for computing the derivative of the composition of functions in your textbook.