# Curve sketching

• June 8th 2009, 01:09 PM
Raoh
Curve sketching
$f(x) = 2\times\ln\left(\exp(x)-2\times\sqrt[]{\exp(x)} + 2\right)$
thanks.(Hi)
• June 8th 2009, 06:47 PM
Amer
Quote:

Originally Posted by Raoh
$f(x) = 2\times\ln\left(\exp(x)-2\times\sqrt[]{\exp(x)} + 2\right)$
$f'(x)>0$ 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