Finding roots of function Consider the function $$f(x)=(2x-9) \cdot 2 \cdot e^{\frac{x^3}{3}-9x+ \frac{46}{3}}$$ Now, the only root to this function is $x=9/2$
I find it quite easy to find this exact root, I will start by saying. Usually i would solve this kind of problem using a CAS. But I would like to know if any of you guys know a way to find the roots by hand.
Probably, what I'm actually looking more for, is a way to show that there are none other roots than $x=9/2$.
Also, I have discovered the fact that $f(x)$ tends to zero as $x$ tends to $-\infty$.
So again, a way to solve $$0=(2x-9) \cdot 2 \cdot e^{\frac{x^3}{3}-9x+ \frac{46}{3}}$$ by hand.
Thanks.

$$e^{\text{anything}} \ne  0$$
