Question

**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.

Answer #1

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

Given the function
h(x)=e^-x^2
Find first derivative f ‘ and second derivative
f''
Find the critical Numbers and determine the intervals
where h(x) is increasing and decreasing.
Find the point of inflection (if it exists) and determine
the intervals where h(x) concaves up and concaves
down.
Find the local Max/Min (including the
y-coordinate)

f(x)= x−cos(x) on the interval [0,2π]
a. Find the Y intercept
b. Is it increasing or decreasing
c. what are the crit points and local minimums and
maximums
d. is it concave up or down
e. what are the inflection points

Given the function g(x) = x3-3x + 1, use the first and second
derivative tests to
(a) Find the intervals where g(x) is increasing and
decreasing.
(b) Find the points where the function reaches all realtive
maxima and minima.
(c) Determine the intervals for which g(x) is concave up and
concave down.
(d) Determine all points of inflection for g(x).
(e) Graph g(x). Label your axes, extrema, and point(s) of
inflection.

Consider the function f(x) =
x^2/x-1 with f ' (x) =
x^2-2x/ (x - 1)^2 and f ''
(x) = 2 / (x - 1)^3 are given. Use these to
answer the following questions.
(a) [5 marks] Find all critical points and determine the
intervals where f(x) is increasing and where it
is decreasing, use the First Derivative Test to fifind local
extreme value if any exists.
(b) Determine the intervals where f(x) is
concave upward and where it is...

1. Use the first derivative test and the second derivative test
to determine where each function is increasing, decreasing,
concave up, and concave down.
y=20x e^-x , x>0
2. Use the first derivative and the second derivative test to
determine where each function is increasing, decreasing, concave
up, and concave down.
y=4sin(πx^2), 10≤x≤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:...

use f(x)=2x^4-4x^2-4 to answer the following.
a) find where f(x) is increasing or decreasing
b) find where f(x) is concave up or down
c) find the coordinates of all relative extrema

f(x)= x^4-2x^2-3. Using the first derivative test, find:
a. All critical Numbers
b. Intervals on which f(x) is increasing or decreasing
c. location and value of all relative extrema

f(x) = 10/cos-1(x). Use calculus to determine: a) all critical
values b) any local extrema c) any absolute extrema d) the
intervals where f is increasing/decreasing e) any points of
inflection rounded to the thousandths place f) intervals where f is
concave up/down

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