Question

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:

Answer #1

Analyze the function f and sketch the curve of f by hand.
Identify the domain, x-intercepts, y-intercepts, asymptotes,
intervals of increasing, intervals of decreasing, local maximums,
local minimums, concavity, and inflection points. f(x) = 3x^4 −
4x^3 + 2

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...

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

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.

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...

Given the function f(x) = x3 - 3x2 - 9x + 10
Find the intervals where it is increasing and
decreasing and find the co-ordinates of the relative maximums &
minimums.
Find the intervals where it is concave up and down and
co-ordinates of any inflection points
Graph the f(x)

f (x) = ex/x2
Find the Domain of f(x)
Does the function have x- or y- intercept of
f(x)?
Find the vertical and horizontal asymptotes.
Find f'(x) and f''(x) .
Find the critical points, find the interval where f(x) is
increasing and decreasing, the interval where f(x) is concave up
and down and the inflection points.

Sketch the graph of the function f(x) = x − 4 / x + 4 using the
guidelines below, a. Determine the domain of f.
b. Find the x and y intercepts.
c. Find all horizontal and vertical asymptotes.
d. Determine the intervals of increasing/decreasing.
e. Determine the concavity of f.

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...

F(x) = ( (x+3)/(x+1) )2
find the domain of F
and any critical numbers, horizontal asymptotes, vertical
asymptotes and points of inflection

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