Question

Let f(x)= (x-2)/(x^2-9)

A. find the x and y-intercepts

B. find the vertical and horizontal asymptote if any

C. find f'(x) and f''(x)

D. find the critical values

E. determine the interval of increasing, decreasing, and find any relative extreme

F. determine the interval which f(x) is concave up, concave down, and any points of inflection

Answer #1

Let
f(x)=(x^2)/(x-2) Find the following
a) Domain of f
b) Intercepts (approximate to the nearest thousandth)
c) Symmetry (Show testing for symmetry)
d) asymptotes
e) Intervals of increase/decrease (approximate the critical
numbers to the nearest thousandth. Be sure to show the values
tested)
f) Local maxima and local minima
g) Intervals of concavity and points of inflection (be sure to
show all testing)
h) summary for f(x)=(x^2)/(x-2)
Domain
X intercepts:
Y intercept:
symmetry:
asymptote:
increasing:
decreasing:
local max:
local min:...

f(x)= (x^2+2x-1)/x^2)
Find the
a.) x-intercept
b.) vertical and horizontal asymptote
c.) first and second derivative
d.) Is it increasing or decreasing? Identify any local
extrema
e.) Is it concave up and down? Identify any points of
reflection.

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.

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.

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...

Find the vertical asymptotes, horizontal asymptote, and x and y
intercepts of the following function and sketch a graph
f(x) = (x^2 − 4) / (x^2 − 2x − 15)

(i) Given the function f(x) = x3 − 3x + 2
(a) What are the critical values of f?
(b) Find relative maximum/minimum values (if any). (c) Find
possible inflection points of f.
(d) On which intervals is f concave up or down?
(e) Sketch the graph of f.
(ii) Find a horizontal and a vertical asymptote of f(x) = 6x .
8x+3

1. You are given the function f(x) = x/(1−x)
a) Find the x and y- intercepts.
b) Find the horizontal asymptote(s).
c) Find the vertical asymptote(s) and do a limit analysis of the
behavior of f on either
side of each vertical asymptote.
d) Find the critical number(s) of f.
e) Find the interval(s) of increase and decrease of f.
f) Find the relative maximum and minimum value(s) of f.
g) Find the hypercritical number(s) of f.
h) Find the...

Given f(x)= x3 -
6x2-15x+30
Determine f ’(x)
Define “critical point” of a function. Then determine the
critical points of f(x).
Use the sign of f ’(x) to determine the interval(s) on which
the function is increasing and the interval(s) on which it is
decreasing.
Use the results from (c) to determine the location and values
(x and y-values of the relative maxima and the relative minima of
f(x).
Determine f ’’(x)
On which intervals is the graph of f(x)...

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

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