f(X)=-2x^3-3x^2-1

Question

i need the increasing and decreasing points for that equation

 

Answer 1

This cubic equation has a local minimum at x = -1, and has a local maximum at x = 0.  These points can be found by taking the derivative of the function, then solving for the zeros:  d/dx (-2x³ - 3x² -1) = -6x² -6x

-6x² - 6x = 0 -->  x(x+1) = 0.  x = {-1, 0}.  If you are not familiar with calculus, you can also find these points by graphing with a graphing calculator.

 

The original function is decreasing on the intervals (-∞, -1) and (0, ∞), and is increasing on the interval (-1, 0)