Consider the function below. (If an answer does not exist, enter DNE.) f(x)-x -
ID: 2886300 • Letter: C
Question
Consider the function below. (If an answer does not exist, enter DNE.) f(x)-x - 12x + 9 (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. 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 (a)-(c) to sketch the araph. Check your work with a graphing device if you have one. 20 ??Explanation / Answer
f(x) = x3-12x +9
f '(x) = 3x2-12
Critical points, f '(x) = 0
3(x2-4)=0
x = -2 ,2
In(-infinity, -2), f '(x) >0
In (-2,2) , f '(x) < 0
In (2 , infinity) , f '(x) >0
INcreasing interval (-infinity,-2)U(2,infinity)
Decreasing interval (-2,2)
Local minimum is at x=2 , which is f(2)= 8-24+9 =-7
Local maximum is at x=-2 which is f(-2) = - 8 +24+ 9 = 25
Inflection point
f ''(x) = 6x
6x=0
x=0 is the inflection point
In (-infinity,0), f ''(x) <0 So concave down
In (0,infinity), f ''(x) >0, so concave up .
Correct graph is the top right graph .