To solve this, you have to know that the first derivative of a function is its slope. When an interval is increasing, it has a positive slope. Thus, we are trying to solve for when the first derivative of a function is positive/negative.
f(x)=2x^3+6x^2-18x+2 f'(x)=6x^2+12x-18 f'(x)=6(x^2+2x-3) f'(x)=6(x+3)(x-1) So the zeroes of f'(x) are at x=1, x=-3 Because there is no multiplicity, when the function passes a zero, he y value is changing signs. Since f'(0)=-18, intervals -3<x<1 is decreasing(because -3<0<1) Thus, every other portion of the graph is increasing. Therefore, you get:
