Question

Suppose that f(x)=x−3x^1/3 (A) Find all critical values of f. If there are no critical values,...

Suppose that

f(x)=x−3x^1/3



(A) Find all critical values of f. 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 f(x) is increasing.

Note: When using interval notation in WeBWorK, you use INF for ∞∞, -INF 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 -1000. 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 -1000. 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 -1000. If there are more than one, enter them separated by commas.
Inflection point(s) at x =

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