Answer: Ok, i will use the hint provided.
We call x1 and x2 to te two mínima of f, that is [tex]\frac{df}{dx} (x1) = 0, \frac{df}{dx} (x2) = 0[/tex].
The convexity condition says that, if f is differentiable, then the graph of f(x) lays above all the tangents between X and Y, if Y>X then
[tex]f(Y) \geq f(X) + f'(X)*(Y-X)[/tex] where [tex]f'(x) = \frac{df}{dx} (x)[/tex].
then, if we took Y = x1 and X = x2, we have [tex]f(x1) \geq f(x2)[/tex] because f'(x2) = 0.
now if we took Y = x2 and X = x1, we have [tex]f(x2) \geq f(x1)[/tex] because f'(x1) = 0.
Then, x1 = x2. Which implies that we only have one minima.
