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I guess this works: Subdivide the interval at 10 to separate the significant oscillatory part from the superexponential decay part. Increase WorkingPrecision to handle the round-off error from the oscillatory part Use the secant method in FindRoot to prevent bad choices for r in trying to numerically approximate the gradient. ?NumericQ protection for rpd[]. ...


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Re or Im are functions that are not differentiable. E.g. consider the following: Limit[(Re[x + I y + del] - Re[x + I y])/del, del -> 0] Limit[(Re[x + I y + I del] - Re[x + I y])/(I del), del -> 0] 1 0 and you see that the value is direction dependent. What can you do? See e.g. in the help about Re. You may use ComplexConjugate or ComplexExpand.


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You must use "Manipulate" and leave out the superfluous (in "Manipulate") "Dynamic". Here is the corrected code: ClearAll[p]; p[m_, n_] := Function[{x}, -7 - m - n + m n + (-7 m - 8 n + 3 m n) x + (10 - 5 m - 8 n + m n) x^2 + (6 - m - 2 n) x^3 + x^4 // Evaluate] Manipulate[ m = pt[[1]]; n = pt[[1]]; r = x /. ...


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