Question

consider the funtion f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2

a) Find the domain of f. (write in interval notation): Df:=_____________?

b) Find the x- and y- intercepts. if any. (write your answers as ordered pairs).

c) Find the asymptotes of f, if any. If there are not, write why. (write answers as equations).

d) Find all of the critical numbers of f. on what intervals is f increasing/decreasing?

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Answer #1

consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?

Graph: f(x)= 2
Find (a) The domain of f.
(b) All asymptotes (write the equations)
(c) X- intercept(s), Y- intercept. Write them as ordered
pairs.
(d) Graph the function. Include asymptotes

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

1. find all vertical asymptotes of function f(x) =
In((e^2In(x))-5x+6)
2. find all x intercepts of the function
g(x)=In((e^2In(x))-3x+5)-In(2)-In(3/2)

given function f(x)=-x^3+5x^2-3x+2
A) Determine the intervals where F(x) Is increasing and
decreasing
b) use your answer from a to determine any relative maxima or
minima of the function
c) Find that intervals where f(x) is concave up and concave
down and any 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:...

1.f(x) = -x^3 -3x^2 +9x-2
Find the value of any relative extreme
2.K(t)=40t/t^2+25
(a) Identify the open intervals where K(t) is increasing.
(b)The function is decreasing on the interval(s)

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:

f(x)=5x^(2/3)-2x^(5/3)
a. Give the domain of f
b. Find the critical numbers of f
c. Create a number line to determine the intervals on which f is
increasing and decreasing.
d. Use the First Derivative Test to determine whether each
critical point corresponds to a relative maximum, minimum, or
neither.

Given the polynomial function f (x) = (x + 3)(x + 2)(x −1)
(a) Write all intercepts as ordered pairs
(b) Find the degree of f to determine end behavior (c) Graph the
function. Label all intercepts

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