Question

please write neatly and use as many papers as it take to form a cohesive and understandable answer with all appropriate steps

Here’s a function f(x) = x^4 - 2x^3 . For f(x), find

(a) (2 points) Domain:

(b) (3 points) Intercepts (if possible)

(c) ( 2 points) End behavior

(d) (2 points) Any vertical or horizontal asymptotes

(e) (8 points) Intervals of increasing/decreasing and Relative max/min and

(f) (8 points) Intervals of concavity and Points of inflection

(g) (10 points) Use all of the above to create a detailed graph of the function (on the given grid). Graphs submitted need to be at least 6” x 6” in size. Do not turn in a tiny graph.

Answer #1

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please write neatly and use as many papers as it take to form a
cohesive and understandable answer with all appropriate steps
Here’s a function f(x) = x^4 - 2x^3 . For f(x), find
(a) (2 points) Domain:
(b) (3 points) Intercepts (if possible)
(c) ( 2 points) End behavior
(d) (2 points) Any vertical or horizontal asymptotes
(e) (8 points) Intervals of increasing/decreasing and Relative
max/min and
(f) (8 points) Intervals of concavity and Points of
inflection
(g) (10...

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

f(x)=x/(x^2)-9
Use the "Guidelines for sketching a curve A-H"
A.) Domain
B.) Intercepts
C.) Symmetry
D.) Asymptotes
E.) Intervals of increase or decrease
F.) Local Maximum and Minimum Values
G.) Concavity and Points of Inflection
H.) Sketch the Curve

Consider the function f(x)=ln(x2
+4)[6+6+8=16 marks]
Note: f'(x) = 2x divided by (x2 +4) f''(x ) =
2(4-x2) divided by (x2+4)2 (I was
unable to put divide sign)
a) On which intervals is increasing or decreasing?
b) On which intervals is concave up or down?
c) Sketch the graph of f(x) Label any intercepts, asymptotes,
relative minima, relative maxima and inflection points.

Consider the function f(x)=ln(x2
+4)[6+6+8=16 marks]
Note: f'(x) = 2x divided by (x2 +4) f''(x ) =
2(4-x2) divided by (x2+4) (I was unable to
put divide sign)
a) On which intervals is increasing or decreasing?
b) On which intervals is concave up or down?
c) Sketch the graph of below. Label any intercepts, asymptotes,
relative minima, relative maxima and inflection points.
.

Given f(x) = , f′(x) = and f′′(x) = , find all possible
x2 x3 x4
intercepts, asymptotes, relative extrema (both x and y values),
intervals of increase or decrease,
concavity and inflection points (both x and y values). Use these
to sketch the graph of f(x) = 20(x − 2)
.
x2

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...

Consider: f(x)=ex-3x^2
Use the graphs of f' and f''.
1) What does the graph of f’ tell you about:
a) asymptotes for f? (exact values and why?)
b) intervals where f is increasing? where f is decreasing?
(exact values and why?)
c) x –values where f has a local minimum? local maximum?
absolute
minimum? absolute maximum? (exact values and why?)
2) What does the graph of f” tell you about:
a) concavity of f? (exact values and why?)
b) inflection...

11) Let p(x) = (4x^2-9)/(4x^2-25)
(a) What is the domain of the function p(x)?
(b) Find all x- and y-intercepts.
(c) Is function p(x) an even or odd function?
(d) Find all asymptotes.
(e) Find all open intervals on which p is increasing or
decreasing.
(f) Find all critical number(s) and classify them into local
max. or local min..
(g) Sketch the graph of p. [Please clearly indicate all the
information that you have found in (a)–(f) above.]

Curve Sketching Practice
Use the information to the side to sketch the graph of
f.
Label any asymptotes, local extrema, and inflection
points.
f is a polynomial function
x
—1
—6
3
—2
6
5
f is a polynomial function
x
1
—4
4
0
7
4

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