Suppose that [math]

(A) Find all critical values of [math]. If there are no critical values, enter -1000. If there are more than one, enter them separated by commas.
Critical value(s) =

(B) Use interval notation to indicate where [math] is increasing.

Note: When using interval notation in WeBWorK, you use I for [math], -I for [math], and U for the union symbol. If there are no values that satisfy the required condition, then enter "{}" without the quotation marks.

Increasing:


(C) Use interval notation to indicate where [math] is decreasing.
Decreasing:


(D) Find the [math]-coordinates of all local maxima of [math]. If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas.

Local maxima at [math] =


(E) Find the [math]-coordinates of all local minima of [math]. If there are no local minima, enter -1000. If there are more than one, enter them separated by commas.

Local minima at [math] =


(F) Use interval notation to indicate where [math] is concave up.
Concave up:


(G) Use interval notation to indicate where [math] is concave down.
Concave down:


(H) Find all inflection points of [math]. If there are no inflection points, enter -1000. If there are more than one, enter them separated by commas.
Inflection point(s) at [math] =

(I) Use all of the preceding information to sketch a graph of [math]. When you're finished, enter a "1" in the box below.

Graph Complete: