Question

f(x) = 1/(x-2) + x - 2

a) Find the vertical and horizontal asymptotes.

b) Find the intervals of increase or decrease.

c) Find the local maximum and minimum values.

d) Find the intervals of concavity and the infection points.

I need help with parts b and d. Step-by-step solutions would be very much appreciated. Thank you for the help in advance!

Answer #1

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

Let f (x) = 2x3 + 3x2 −12x + 6.
(1) Find the intervals of increase or decrease.
(2) Find the local maximum and minimum values.
(3) Find the intervals of concavity and the inflection points.
(d) Use the information from parts (a)-(c) to sketch the graph

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...

If f(x)-x^3-3x;
a) find the intervals on which f is increasing or
decreasing.
b)find the local maximum and minimum values
c)find the intervals of concavity and inflection points
d)use the information above to sketch and graph of f

Please find all of horizontal asymptotes and vertical asymptotes
of function f(x) = [−7x^2 * (x − 2)^2 ]/ [ 3(x + 1)^3 * (x −
2)]

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...

2. Given that ?(?) = ??−??−?/???+??
a. Find Vertical and horizontal asymptotes.
b. Graph h(x)

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

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:...

(a) Find horizontal and vertical asymptotes of f(x) = 2 + x 2 −
3x 6 x 6 − x 3
(b) Find lim x→−∞ −2x 5 − 3x 2 + x − 1 1 − x 3 − 3x 5

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