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 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:

Answer #1

Suppose that f(x)=x^4-3x^3.
(A) List all the critical values of f(x). Note: If there are no
critical values, enter 'NONE'
(B) Use interval notation to indicate where f(x) is
increasing.
Note: Use 'INF' for ∞, '-INF' for −∞, and use 'U'
for the union symbol.
(C) Use interval notation to indicate where f(x) is
decreasing.
(D) List the xx values of all local maxima of f(x). If there are
no local maxima, enter 'NONE'.
(E) List the xx values of...

Suppose that f(x)=6/x^2−25. (A) List all critical numbers of f.
If there are no critical numbers, enter 'NONE'. (B) Use interval
notation to indicate where f(x) is increasing. Note: Use 'Inf' for
∞, '-Inf' for −∞, and use 'U' for the union symbol. (C) Use
interval notation to indicate where f(x) is decreasing. (D)List the
x-coordinates of all local maxima of f. If there are no local
maxima, enter 'NONE'. (E) List the x-coordinates of all local
minima of f....

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....

Let f(x)=4+12x−x^3. Find (a) the intervals on which ff is
increasing, (b) the intervals on which ff is decreasing, (c) the
open intervals on which ff is concave up, (d) the open intervals on
which f is concave down, and (e) the x-coordinates of all
inflection points.
(a) f is increasing on the interval(s) =
(b) f is decreasing on the interval(s) =
(c) f is concave up on the open interval(s) =
(d) f is concave down on the...

Consider the function
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

Given f(x)= x3 -
6x2-15x+30
Determine f ’(x)
Define “critical point” of a function. Then determine the
critical points of f(x).
Use the sign of f ’(x) to determine the interval(s) on which
the function is increasing and the interval(s) on which it is
decreasing.
Use the results from (c) to determine the location and values
(x and y-values of the relative maxima and the relative minima of
f(x).
Determine f ’’(x)
On which intervals is the graph of f(x)...

For the function f(x)=−3x^3+36x+6
(a) Find all intervals where the function is
increasing.
Answer: ff is increasing on=
(b) Find all intervals where the function is
decreasing.
Answer: ff is decreasing on=
(c) Find all critical points of f(x)
Answer: critical points: x=
Instructions:
For parts (a) and (b), give your
answer as an interval or a union of intervals, such as
(-infinity,8] or (1,5) U
(7,10) .
For part (c), enter your xx-values as a
comma-separated list, or none...

Analyze and sketch the graph of the function f(x) = (x −
4)2/3
(a) Determine the intervals on which f(x) is increasing /
decreasing
(b) Determine if any critical values correspond to a relative
maxima / minima
(c) Find possible inflection points
(d) Determine intervals where f(x) is concave up / down

Consider the following. (If an answer does not exist, enter
DNE.)
f '(x) =
x2 + x − 30
(a)
Find the open intervals on which f ′(x) is
increasing or decreasing. (Enter your answers using interval
notation.)
increasing
(−12,∞)
decreasing
(−∞,−12)
(b)
Find the open intervals on which the graph of f is
concave upward or concave downward. (Enter your answers using
interval notation.)
concave upward
concave downward
(c)
Find the x-values of the relative extrema of
f. (Enter...

For f(x) = 2x4 - 4x2 + 1 find the open
intervals in which the function is increasing and decreasing.
Find open intervals where the function is concave up and concave
down.
Sketch the graph of the function - label all local maximums, all
local minimums, and any inflection points.

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