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FindMinimum

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FindMinimum[f, {x, $x_0$}]

searches for a numerical minimum of f, starting from x=$x_0$.

FindMinimum by default uses Newton's method, so the function of interest should have a first derivative.

• • FindMinimum[(x-3)^2+2., {x, 1}]

• • FindMinimum[10*^-30 *(x-3)^2+2., {x, 1}]

• • FindMinimum[Sin[x], {x, 1}]

• • phi[x_?NumberQ]:=NIntegrate[u,{u,0,x}, Method->"Internal"];

• • Quiet[FindMinimum[phi[x]-x,{x, 1.2}, Method->"Newton"]]

• • Clear[phi];

For a not so well behaving function, the result can be less accurate:

• • FindMinimum[Exp[-1/x^2]+1., {x,1.2}, MaxIterations->10]