Reference no: EM131724879

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 =