I have such function f(x) = x^6(x-4)^3 for the interval [-11, 10],
I need to evaluate on which intervals the function is increasing, on which one is positive and where is the minimum.
I tied to find the derivative , so f'(x) = 6x^5(x-4)^3*3(x-4)^2*x = and wrote it as 18x^6(x-4)^3(x-4)^2
even before calculating the critical points it seems that I complicate something,
Could you help me by indicating one simpler way of factoring and differentiating this?