I am having trouble finding a compact formula for y'', so that I can place it on my sign table, but instead i got a really long equation which is too big
hi
Yeah , i tried the second derivative too and ended up with sth really long and uninteresting .
Fisrtly , find its first derivative which is
$\displaystyle y'(x)=\frac{e^{-\frac{1}{3}x}(x-1)}{3x^{\frac{2}{3}}}$
when y'(x)=0 , x=1
Make a table calculating dy/dx for 1 , 1^- , 1^+
this point (1 , $\displaystyle \frac{1}{e^{\frac{1}{3}}}$) is a local maximum .
And also the graph passes thought point (0,0)
Lets take a look at the behaviour of the graph as it goes to +/- infinity
when x approaches +ve infinity , y approaches 0
When x approaches -ve infinity , y approaches -ve infinity .
And it seems that (0,0) is a point of inflexion here .