SOLUTION: I need help with this question. Determine the intervals of increasing and decreasing for each of the following functions. a)f(x)=x^3-3x^2-9x+4 b)f(x)=5+36x-3x^2-2x^3

Question 1170706: I need help with this question.
Determine the intervals of increasing and decreasing for each of the following functions.
a)f(x)=x^3-3x^2-9x+4
b)f(x)=5+36x-3x^2-2x^3
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)=x^3-3x^2-9x+4
derivative is 3x^2-6x-9
set equal to 0, and divide by 3 so x^2-2x-3=0=(x-3)(x+1)
so critical points are at x= -1 and x=3
when x < -1, the function gets more negative, therefore, from (-oo, -1) the function is increasing,
from -1 < x < 3 it is decreasing,
and from (3, oo) it is increasing.

f(x)=-2x3-3x^2+36x+5
f'(x)=-6x^2-6x+36 set equal to 0 divide by -6 and x^2+x-6=0
x^2+x-6=0
x=(x+3)(x-2)
critical points are x=-3, 2
so it is decreasing on the interval (-oo, -3),
increasing on the interval (-3, 2),
and decreasing on the interval (2, oo)

The term with the highest power is what drives the function at infinity.

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