Suppose that f(x)=x^(1/3)(x+3)^(2/3)
(A) Find all critical values of ff. If there are no critical values, enter None. If there are more than one, enter them separated by commas.
Critical value(s) =
(B) Use interval notation to indicate where f(x) is increasing.
Note: Use I for ∞, -I for -∞, 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 f(x) is decreasing.
Decreasing:
(D) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter None. If there are more than one, enter them separated by commas.
Local maxima at x =
(E) Find the x-coordinates of all local minima of f. If there are no local minima, enter None. If there are more than one, enter them separated by commas.
Local minima at x =
(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) Find all inflection points of f. If there are no inflection points, enter None. If there are more than one, enter them separated by commas.
Inflection point(s) at x =