I am trying to understand how to find the maximum rate of change when say there is a given gradient of the function. My cubic function is:
$$f(x) = -\frac{7}{4000}x^{3}+\frac{269}{400}x^{2}-\frac{1717}{20}x+3570 $$
Tnd the gradient needs to be between $-5$ and $5$. This is as far as I understand to find the gradient we differentiate the cubic then find the $x$ values for it and that gives us our gradient. When I do this I get value like x=130. This is the part that confuses me and I am not sure where to go from here.