Question

Determine the inflection points of f(x)=x-lnx if any !!! HELP PLEASE THANK YOU

Answer 1

this is what I got for my second derivative

Answer 2

maybe it should be positive

Answer 3

\[\large f(x) = x-\ln(x)\]\[\large f'(x) = 1 - \frac{1}{x}\]\[\large f'(x)=1-1x^{-1}\]\[\large f''(x) = 0+(-1)(-1)x^{-2}\]\[\large f''(x)=\frac{1}{x^2}\]

Answer 4

how can I set this to zero?

Answer 5

Now set \(\large \frac{1}{x^2}\) to 0 and solve for x to find inflection points. \[\large \frac{1}{x^2}=0\] Since you annot solve for this there is no solution. \[\large 1 = (0)(x^2) \]\[\large 1 \ne 0\]

Answer 6

so does this mean no inflection points?

Answer 7

Mmhmm.

Answer 8

thanks for the help!

Answer 9

No problem :) You can also check to see if there are inflection points by checking where the graph changes concavity. (i.e concave up \(\rightarrow\) concave down, or concave down \(\rightarrow\) concave up)