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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