SOLUTION: The function f(x)=4x^(3)−6x^(2)−672x−8 is decreasing on the interval (? , ?). It is increasing on the interval ( −∞, ? ) and the interval ( ? , &

Algebra ->  Linear-equations -> SOLUTION: The function f(x)=4x^(3)−6x^(2)−672x−8 is decreasing on the interval (? , ?). It is increasing on the interval ( −∞, ? ) and the interval ( ? , &      Log On


   

Question 1112034: The function
f(x)=4x^(3)−6x^(2)−672x−8
is decreasing on the interval (? , ?).
It is increasing on the interval ( −∞, ? ) and the interval ( ? , ∞ ).
The function has a local maximum at ?.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=4x^(3)−6x^(2)−672x−8
f'(x)=12x^2-12x-672; f''(x)=24x-12
Set equal to 0 and factor out a 12
12(x^2-x-56)=0=12(x-8)(x+7)
x=8, -7, which are critical points.
when x=8, f''(x)=180, a minimum
when x=-7, f''(x)=-180, a maximum. The local maximum is at (-7, 3030)
it goes from -oo to -7, increasing, decreases on the interval (-7, 8) and increases on the interval (8, oo)
graph%28300%2C300%2C-20%2C30%2C-4000%2C4000%2C4x%5E3-6x%5E2-672x-8%29