After plotting the graph of $$f(x)=\frac{π}{3\sqrt{2 π}} (\frac{e^{\frac{-x^2}{18}}}{3} + \frac{e^{\frac{-(x - 5)^2}{2}}}{1} +\frac{e^{\frac{-(x - 15)^2}{8}}}{2} ) (1 + x^2)$$
I would like to verify with mathematica that $f(x)<20$, for $\vert{x}\vert>20$ . So I write in the notebook:
Solve[π/(3 Sqrt[2 π]) (E^(-x^2/18)/3 + E^(-(x - 5)^2/2) +
E^(-(x - 15)^2/8)/2) (1 + x^2) < 10 && Abs[x] > 20, Reals]]]
and then I get the message that
Solve::fulldim: The solution set contains a full-dimensional component; use Reduce for complete solution information.
On the other hand WolphramAlfa gives me the answer.
Can you please tell me what I did wrong here? Is there another way to check this inequality? Thanks.
Maximize[{f[x], Abs[x] > 20}, x, Reals] // Simplify // Quiet
indicates that forAbs[x] > 20
the function is below about3.6803
$\endgroup$ – Bob Hanlon Oct 29 '19 at 20:56