# How to solve x*e^2x=4 (1 Viewer)

#### Squar3root

##### realest nigga
Oops, don't know how that happened. It's edited now.
i think post #17 stuffed up

#### girlworld_club

##### Member
hmmm, it appears that i may have been wrong. when i did it my way, i just drew a rough graph and assumed it was so *dusts hands* but now that i do it algebraically; let f(x)=1/x^2 +1

f''(x)= (2*(3*x^2-1))/(x^2+1)^3 [used wolframalpha caz i didn't want to make a mistake and i am too lazy to write it out by hand]

so it is concave up when f''(x) >0 when i solve this i get 1/root(3) and since f(x) is even hence the other side is the same

so from -infinity to -1/root(3) the graph is concave up; from -1/root(3) to 1/root(3) the graph is concave down and from 1/root(3) to infinity the graph is concave up. note that x= +- 1/root(3) are points of inflexion

Edit: this may help: http://www.wolframalpha.com/input/?i=1/(x^2++1)
That's what i got, the book completely stuffed me up for 2 hours thinking i was wrong.

P.s THANKS HEAPS

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#### girlworld_club

##### Member
But did you differentiate TWICE?
Yep All good everything has been solved.

#### Squar3root

##### realest nigga
That's what i got, the book completely stuffed me up for 2 hours thinking i was wrong.

P.s THANKS HEAPS
some rep would be nice

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