Question

How do you determine the intervals for which the function is increasing or decreasing given `f(x)=x^3+3x^2-9x`?

Answer 1

We differentiate the function to find an expression for its slope: `f'(x)=3x^2+6x-9`. The function is increasing when its slope (gradient) is positive `(f'(x)>0)` and decreasing when its slope is negative `(f'(x)<0)`.