Question

Consider the function f(x*)=ln(x ^{2}*
+4)[6+6+8=16 marks]

Note: f'(x) = 2x divided by (x^{2} +4) f''(x ) =
2(4-x^{2}) divided by (x^{2}+4)^{2} (I was
unable to put divide sign)

a) On which intervals is increasing or decreasing?

b) On which intervals is concave up or down?

c) Sketch the graph of f(x) Label any intercepts, asymptotes, relative minima, relative maxima and inflection points.

Answer #1

Consider the function f(x)=ln(x2
+4)[6+6+8=16 marks]
Note: f'(x) = 2x divided by (x2 +4) f''(x ) =
2(4-x2) divided by (x2+4) (I was unable to
put divide sign)
a) On which intervals is increasing or decreasing?
b) On which intervals is concave up or down?
c) Sketch the graph of below. Label any intercepts, asymptotes,
relative minima, relative maxima and inflection points.
.

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

Let f(x)=6x^2−2x^4. Find the open intervals on which f is
increasing (decreasing). Then determine the x-coordinates of all
relative maxima (minima).
1.
f is increasing on the intervals
2.
f is decreasing on the intervals
3.
The relative maxima of f occur at x =
4.
The relative minima of f occur at x =

Consider the function
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

question #1: Consider the following function.
f(x) =
16 − x2,
x ≤ 0
−7x,
x > 0
(a) Find the critical numbers of f. (Enter your answers
as a comma-separated list.)
x =
(b) Find the open intervals on which the function is increasing or
decreasing. (Enter your answers using interval notation. If an
answer does not exist, enter DNE.)
increasing
decreasing
question#2:
Consider the following function.
f(x) =
2x + 1,
x ≤ −1
x2 − 2,
x...

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

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

4. Given the function y = f(x) = 2x^3 + 3x^2 – 12x +
2
a. Find the intervals where f is increasing/f is
decreasing
b. Find the intervals where f is concave up/f is concave
down
c. Find all relative max and relative min (state which
is which and why)
d. Find all inflection points (also state
why)

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:

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:...

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