Solve contains wrong solution
Hello, I tried to following to find a maxima of a function:
var('t x'); f=(e^(x*t))*(x-1)^2; maxima = solve([derivative(f,x)==0, derivative(f,x,2)<0],x) show(maxima);
And the solution sage spits out are:
[ [x == 1, -2 > 0], [x == (t - 2)/t, -(t - 2)^2 + 2*(t - 2)*t - t^2 + 6 > 0] ]
I understand that sage cannot evaluate the validity of the second solution but the first one surely is no solution at all.
Why does it give me this solution or am I doing anything wrong?