SOLUTION: find the intervals on which f(x)= 2x^3 - 3x^2 is increasing. find the intervals on which f(x)= 2x^3 - 3x^2 is concave down.

Algebra ->  Trigonometry-basics -> SOLUTION: find the intervals on which f(x)= 2x^3 - 3x^2 is increasing. find the intervals on which f(x)= 2x^3 - 3x^2 is concave down.      Log On


   

Question 1059519: find the intervals on which f(x)= 2x^3 - 3x^2 is increasing.
find the intervals on which f(x)= 2x^3 - 3x^2 is concave down.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
first derivative
6x%5E2-6x=0
x%5E2-x=0
x%28x-1%29=0

Know the basic shape of cubic polynomial or function!
Maximum at x=0 and minimum and x=1.
You can figure the intervals of the function increasing.

Second derivative
12x-6
12x-6=0
2x-1=0
2x=1
x=1%2F2-----------this is where you find the inflection point, and again, understanding the shape of cubic functions, the interval on which f is concave downward is (-infinity, 1/2 ).