# Thread: Curve sketching

1. ## Curve sketching

hi,would you please help me graph this function,i'm really having problems .
$f(x) = 2\times\ln\left(\exp(x)-2\times\sqrt[]{\exp(x)} + 2\right)$
thanks.

2. Originally Posted by Raoh
hi,would you please help me graph this function,i'm really having problems .
$f(x) = 2\times\ln\left(\exp(x)-2\times\sqrt[]{\exp(x)} + 2\right)$
thanks.
find where dose your curve intersect with x-axis(y=0) and y-axis(x=0)
then find the critical points and the increasing intervals and decreasing intervals increasing intervals

$f'(x)>0$ decreasing intervals $f'(x)<0$

then find the concavity up or down the curve concave up when $f''(x)>0$ and concave down when $f''(x)<0$ then plot the critical points and the points where the curve intersect with the axes and the inflection points after that draw you curve according to the intervals of increasing and intervals of concavity

3. thanks a lot for your help .