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FindMaximum

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

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

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

• • FindMaximum[-(x-3)^2+2., {x, 1}]

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

• • FindMaximum[Sin[x], {x, 1}]

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

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

• • Clear[phi];

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

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