I was working on this problem as a demonstration for Methods
g[x_] = Sin[x]/E^x;
Reduce[g'[x] == 0, x] produces
C[1] \[Element] Integers && (x == -2 ArcTan[1 + Sqrt[2]] + 2 \[Pi] C[1] ||
x == -2 ArcTan[1 - Sqrt[2]] + 2 \[Pi] C[1])
Solve[g'[x] == 0, x] produces the first solutions between -Pi and Pi {{x -> -((3 [Pi])/4)}, {x -> [Pi]/4}}
Solve[{g'[x] == 0, 0 <= x <= 4 Pi}, x] produces something similar to the reduce answer {{x -> 2 \[Pi] -
2 ArcTan[1 - Sqrt[2]]}, {x -> -2 ArcTan[1 - Sqrt[2]]}, {x ->
2 \[Pi] - 2 ArcTan[1 + Sqrt[2]]}, {x ->
4 \[Pi] - 2 ArcTan[1 + Sqrt[2]]}}
I would like to know why it isn't producing the simpler solution x=(kPi+1)/4 k element of integers
Also I wondered why Mathematica joins the graph of h'[x] at 2 for the hybrid function
h[x_] = Piecewise[{{-4, x <= 0}, {x^2 - 4, 0 < x < 2}, {x - 2,
x >= 2}}];
when it is not continuous.