Question

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.]

Answer #1

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...

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.

f(x)=2x ln x
find what intervals on the graph of the function are increasing
and decreasing and identify local max and min points

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.

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.

) Let
.f'(x)=x2-4x-5
Determine the interval(s) of x for which the function
is increasing, and the interval(s) for which the function is
decreasing.
Find the local extreme values of f(x) , specifying
whether each value is a local maximum value or a local minimum
value of f.
Graph a sketch of the graph with parts (a) and (b) labeled

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

f(x)= -4x/ x^2+4
i think i found the first dervivative: f'(x)=
(4x^2-16)/(x^2+4)^2
but im not sure if thats right and then i get confused after
that on how i find the critical numbers: x=____
i think i got x=2 for the critical number
then i am supposed to find where it is increasjng and
decreasing and i dont understand the steps on how to find that out-
i understand the number line but how do you plug in the
numbers...

For f(x) xe-x
( a) Find the local extrema by hand using the first derivative
and a sign chart. b) Find the open intervals where the function is
increasing and where it is decreasing. c) Find the intervals of
concavity and inflection points by hand. d) Sketch a reasonable
graph showing all this behavior . Indicate the coordinates of the
local extrema and inflections.

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.

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