h[x_] = x^3 +x^2+ k;(adsbygoogle = window.adsbygoogle || []).push({});

Solve[h[x] == 0, k]

{{k -> -x^2 - x^3}}

Reduce[Abs[h'[x]] >= 1, x]

Re[x] < -(1/2) || (-(1/2) <= Re[x] <= 1/2 && (Im[x] <= -(1/2) Sqrt[1 - 4 Re[x]^2] ||

Im[x] >= 1/2 Sqrt[1 - 4 Re[x]^2])) || Re[x] > 1/2

Now i want to express these inequalities in terms of the value of k i obtained earlier, how can i do this, i have tried the mathematica online resource but i havn't been able to figure it out.

Reduce[Abs[h'[x]] >= 1, k]

gives me the following output:

Abs[-1 + 2 x] >= 1

whereas i want my solution in terms of k

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# Solutions to equation

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