Question

# Suppose that f(x)=4x2ln(x),x>0.f(x)=4x2ln⁡(x),x>0. (A) List all the critical values of f(x)f(x). Note: If there are no...

Suppose that

f(x)=4x2ln(x),x>0.f(x)=4x2ln⁡(x),x>0.

(A) List all the critical values of f(x)f(x). Note: If there are no critical values, enter 'NONE'.

(B) Use interval notation to indicate where f(x)f(x) is increasing.
Note: Use 'INF' for ∞∞, '-INF' for −∞−∞, and use 'U' for the union symbol. If there is no interval, enter 'NONE'.
Increasing:

(C) Use interval notation to indicate where f(x)f(x) is decreasing.
Decreasing:

(D) List the xx values of all local maxima of f(x)f(x). If there are no local maxima, enter 'NONE'.
xx values of local maximums =

(E) List the xx values of all local minima of f(x)f(x). If there are no local minima, enter 'NONE'.
xx values of local minimums =

(F) Use interval notation to indicate where f(x)f(x) is concave up.
Concave up:

(G) Use interval notation to indicate where f(x)f(x) is concave down.
Concave down:

(H) List the xx values of all the inflection points of ff. If there are no inflection points, enter 'NONE'.
xx values of inflection points =

(I) Use all of the preceding information to sketch a graph of ff. Include all vertical and/or horizontal asymptotes. When you're finished, enter a "1" in the box below.
Graph complete:

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