SOLUTION: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x)=x^4/4 +x^3 +x^2

Algebra ->  Test -> SOLUTION: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x)=x^4/4 +x^3 +x^2      Log On


   

Question 1155972: Find the intervals on which f is increasing and the intervals on which it is decreasing.
f(x)=x^4/4 +x^3 +x^2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=x%5E4%2F4+%2Bx%5E3+%2Bx%5E2
find first derivative:
f′%28x%29=4x%5E3%2F4+%2B3x%5E2+%2B2x
f′%28x%29=x%5E3+%2B3x%5E2+%2B2x
f′%28x%29=x%28x%5E2+%2B3x%2B2%29
If f′%28x%29+%3E+0, then f is increasing on the interval:

x%28x%5E2+%2B3x%2B2%29%3E+0
x%3E+0
or
x%5E2+%2B3x%2B2%3E+0
%28x+%2B+1%29+%28x+%2B+2%29%3E0
x%3E-1 or x%3E-2

f is increasing on the intervals:
(-2,-1) U (0,infinity)

and f is decreasing on the interval:
(-infinity,-2) U (-1,0)


+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E4%2F4+%2Bx%5E3+%2Bx%5E2%29+