Here is my function:
f[x_] := x^2 + k*x
I can plot this function to see its behavior but I certainly cannot obtain an answer by this visualization
Plot3D[f[x], {x, 0, 10}, {k, 0, 10}]
I will eventually create a loop for the question at hand, but I want to know what that k value would be in advance before I begin creating my loop that'll find k for me. I guess you could say I'm trying to work backwards.
I tried creating a table (by hand) starting at x = 0, then finding what that equation for f(x) is, then using arbitrary k values to try and come up with something. I'm not sure how I would go about finding a slope from that though.
UPDATE
slope[m_] := (
f[x_] := x^2 + k*x;
g[x_] = D[f[x], x] /. x -> Sqrt[k];
k = 1;
While[g[x] < m, k; k++];
k)
slope[20]
f'[Sqrt[k]]
and solve for where they're equal withSolve[]
. $\endgroup$