Consider the function below. (If you need to use -infinity or infinity, enter -I

Question

Consider the function below. (If you need to use -infinity or infinity, enter -INFINITY or INFINITY.)
h(x) = (x + 1)3 - 3x - 2
(a) Find the intervals of increase. (Enter the interval that contains smaller numbers first.)
( , ) union ( , )

Find the interval of decrease.
( , )

(b) Find the local minimum value.


Find the local maximum value.


(c) Find the inflection point.
( , )

Find the interval the function is concave up.
( , )

Find the interval the function is concave down.
( , )

(d) Use this information to sketch the graph of the function. (Do this on paper. Your instructor may ask you to turn in this graph.)

Explanation / Answer

h(x) = (x + 1)3 - 3x - 2 h'(x)=3(x+1)^2-3=0 x=0,-2 increasing (-infinity,-2)U(0,infinity) decreasing (-2,0)

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