Consider the equation below. f(x) = 4x3 + 12x2 - 96x + 8 (a) Find the intervals
ID: 2897962 • Letter: C
Question
Consider the equation below.f(x) = 4x3 + 12x2 - 96x + 8
(a) Find the intervals on which f is increasing. (Enter your answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer using interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c) Find the inflection point.
(x, y) =
Find the interval on which f is concave up. (Enter your answer using interval notation.)
Find the interval on which f is concave down. (Enter your answer using interval notation.)
Explanation / Answer
f(x) = 4x^3 + 12x^2 - 96x + 8
f'(x)=12x^2 +24x-96=12(x^2+2x-8)=0, 12(x+4)(x-2)= x=-4, x=2
f is increasing in (-,-4)U(2,+)
f is decreasing in (-4,2)
B) local minimum value (2,-104)
local maximum value (-4,328)
C) f''(x)=12(2x+2)=0 , x=-1 inflección (-1,112)
Find the interval on which f is concave up (-1,+)
Find the interval on which f is concave down. (-,-1)