Question

Use the function ?(?) = ?4 − 4?3 for questions 12 – 14.

12. Find where ?(?) is increasing and decreasing. Then state the
local maximum and minimum values.

B. Find where ?(?) is concave up and concave down. Then state the inflection points.

C. Find the x- and y- intercepts of ?(?). State any vertical and horizontal asymptotes, if there are any. Then sketch the graph of ?(?) using the information from questions 12 and 13, along with the newly found information. Clearly identify all crucial points and asymptotes.

Answer #1

For the function
f(x) =x(x−4)^3
•
Find all
x-intercepts and find the
y-intercept
•
Find all critical numbers,
•
Determine where the function is increasing and where it is
decreasing,
•
Find and classify the relative extrema,
•
Determine where the function is concave up and where it is
concave down,
•
Find any inflection points, and Use this information to sketch
the graph of the function.
•
Use this information to sketch the graph of the function.

Question 1
With: ?(?) = ?3 + 4 ?2
What is the domain of ??
Find the equations of all the asymptotes of ? (if any) (at the
boundaries/holes of the domain)
Find the intercepts of ? (if any)
Is the function even? Odd? If yes, what symmetry will the graph
possess?
Do a sign chart of the first derivative, indicate the intervals
where ? is increasing/decreasing, and
find all the horizontal tangents of ? (if any).
Do a sign...

Analyze and plot the graph of f(x)= x^4/2 - 2x^3/3. for this,
find;
1) domain of f:
2)Vertical asymptotes:
3) Horizontal asymptotes:
4) Intersection in y:
5) intersection in x:
6) Critical numbers
7) intervals where f is increasing:
8) Intervals where f is decreasing:
9) Relatives extremes
Relatives minimums:
Relatives maximums:
10) Inflection points:
11) Intervals where f is concave upwards:
12) intervals where f is concave down:
13) plot the graph of f on the plane:

For the function f(x)=x^5+5x^4-4. Write "none" if there isn't an
answer.
(a) find all local extrema of this function, if any, and
increasing and decreasing intervals.
Local max:___ Local min:___ Increasing:___ Decreasing:___
(b) Find all the inflection points of this function, if ay. And
concave up and concave down intervals.
Inflection points:___ concave up:___ concave down:___
(c) Use part a and b to sketch the graph of the function. Must
label important points and show proper concavity.

Let g (x) = [(x^2-3)/(x^3)]
(a) Determine (if they exist) the vertical and horizontal
asymptotes of g.
(b) Find the formula for g′ (x) and g′′ (x).
(c) Find (if they exist) the local extremes of g.
(d) Find (if they exist) the inflection points of g.
(e) Determine the intervals where g is increasing, and where g
is decreasing.
(f) Determine the intervals where g is concave upward, and
where g is
concave down.
(g) Plot the graph of...

7. Sketch complete graphs of the following; indicate where the
function is increasing/decreasing, has local extrema, where the
graph is concave up or concave down, asymptotes and coordinate
intercepts
(a) ?(?)=(1/5)?5−? (b) ?(?)=(3?+2)/?

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.

Find the intervals where the function ?(?) = ? 3 + 15? 2 − 72? −
610 is increasing, decreasing and the value(s) where it has
extrema. Give the intervals where in its concave up, concave down,
and inflection point. Use this information to sketch a graph of the
function.

Consider the function ? where ?(?)=4?ln(?)?2.
For which real numbers is ?(?) defined? That is, what is the
domain?
Find any intercepts of ?(?).
Find any vertical or horizontal asymptotes of ?.
Find the intervals on which ? is increasing and on which ? is
decreasing.

?(?)=4?^3/?^?, ?∈(−∞,∞)
a. Find ?′(?), and show how to use the First Derivative Test to
find the intervals of increasing/decreasing, as well as the
locations of any local maximums and/or minimums.
b.Find ?′′(?), and show how to use the Concavity Test to find
the intervals of concave up and concave down, as well as the
locations of any inflection points.
c.Make a list of all local extrema and inflection points, given
as (?,?)coordinates(leave x-values exact, in terms of ?; round...

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