Over which interval is f(x) = x^3 - 12x^2 + 36x + 1 decreasing?
We set y' = 3x^2 - 24x + 36 = 0 and solve for x
3x^2 - 24x + 36 = 0
implies that x^2 - 8x + 12 = 0
implies that x^2 - 8x ...
A function can be increasing or decreasing in an interval. To ascertain the intervals of increase or decrease the derivative test is used as illustrated in this problem.