(15 points) Suppose that f(x) = x4 – 7x3. (A) List all the critical values of f(x). Note: If there are no critical values, enter 'NONE'.
(B) Use interval notation to indicate where f(x) is increasing.
Note: Use 'INF' for o, '-INF' for -00, and use 'U' for the union symbol.
Increasing:
(C) Use interval notation to indicate where f(x) is decreasing.
Decreasing:
(D) List the x values of all local maxima of f(x). If there are no local maxima, enter 'NONE'.
x values of local maximums =
(E) List the x values of all local minima of f(x). If there are no local minima, enter 'NONE'.
x values of local minimums = (F) Use interval notation to indicate where f(x) is concave up.
Concave up:
(G) Use interval notation to indicate where f(x) is concave down.
Concave down:
(H) List the x values of all the inflection points of f. If there are no inflection points, enter 'NONE'.
x values of inflection points =
(1) Use all of the preceding information to sketch a graph of f. When you're finished, enter a "1" in the box below.