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2012-12-02 05:16:16 +0100 commented question Solve contains wrong solution

I know, that I could only solve for f'(x)==0 and filter for f''(x)<0 but solve shouldn't contain solutions like that, I think.

2012-12-02 04:50:28 +0100 commented answer Solve contains wrong solution

surely there must be something slightly off with this solution because for x=1 y is always 0. Only the local maximum at (t - 2)/t changes.

2012-12-01 22:14:02 +0100 asked a question 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?