Question

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 open interval(s) =

(e) the xx coordinate(s) of the points of inflection are =

**Notes:** In the first four boxes, your answer
should either be a single interval, such as [0,1), a comma
separated list of intervals, such as (-inf, 2), (3,4], or the word
"none".

In the last box, your answer should be a comma separated list of xx values or the word "none".

Answer #1

3 parts
following these instructions
Find the critical numbers for f and the open intervals on which
f is increasing (decreasing)
For the first question, your answer should be a comma-separated
list of x values or the word "none". For the other two, your answer
should either be a single interval, such as (0,1), a
comma-separated list of intervals, such as (-inf, 2), (3,4), or the
word "none".
answeres needed for each
1.
The critical numbers for f are
2. ...

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...

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...

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

Let f(x)=2x^3 - 9x^2 +12x -4
Find the intervals of which f is increasing or decreasing
Find the local maximum and minimum values of f
Find the intervals of concavity and the inflection points

1. Let ?(?)=−?4−4?3+8?−1. Find the open intervals on which ? is
concave up (down). Then determine the ?-coordinates of all
inflection points of ?.
2. Find the x-values of all inflection points for the graph
?(?)=2?4+18?3−30?2+15f(x)=2x4+18x3−30x2+15. (Give your answers as a
comma separated list, e.g., 3,-2.)
3. Let f(x)=1/4x2+7. Find the open intervals on which ?f is
concave up (down). Then determine the ?x-coordinates of all
inflection points of ?.
4. Let ?(?)=6?−3/?+4 Find the open intervals on which ?f...

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.

4. Given the function y = f(x) = 2x^3 + 3x^2 – 12x +
2
a. Find the intervals where f is increasing/f is
decreasing
b. Find the intervals where f is concave up/f is concave
down
c. Find all relative max and relative min (state which
is which and why)
d. Find all inflection points (also state
why)

Let f(x) = x3 + 3x2 - 24x - 10
a) Find the intervals on which f is increasing/decreasing, and
find all local maximum and local minimum values of f.
b) Find all intervals on which f is concave up/concave down, and
find all inflection points of f.

Find the intervals where f(x) = 2x3 + 3x2
- 36x + 7 is increasing, decreasing, concave up, concave down, and
the inflection points.

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