Consider the function below. (if an answer does not exist, enter dne.) f(x) = x3 − 12x + 8 (a) find the interval of increase. (enter your answer using interval notation.) find the interval of decrease. (enter your answer using interval notation.) (b) find the local minimum value(s). (enter your answers as a comma-separated list.) find the local maximum value(s). (enter your answers as a comma-separated list.) (c) find the inflection point. (x, y) = find the interval where the graph is concave upward. (enter your answer using interval notation.) find the interval where the graph is concave downward. (enter your answer using interval notation.) (d) use the information from parts () to sketch the graph. check your work with a graphing device if you have one.

a) DNE

b) Decreasing (-2,2) and Increasing(-∞, -2) and (2, ∞)

c) Concave up from (2, ∞) and downward from (-∞, 2).

d) See attached picture.

Step-by-step explanation:

The function x³ - 12x + 8 is a cubic function. Cubic functions do not have asymptotic behavior. There are no vertical or horizontal asymptotes. According to its graph attached below, the function starts by increasing from negative infinity to a peak at -2. At the peak it changes to decreasing from -2 to 2. At this valley it increases from 2 to infinity. This is written as (-∞, -2), (-2,2) and (2, ∞). It is concave up from (2, ∞) and downward from (-∞, 2).

a) DNE

b) Decreasing (-2,2) and Increasing(-∞, -2) and (2, ∞)

c) Concave up from (2, ∞) and downward from (-∞, 2).

d) See attached picture.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x