Question

Given f(x) = , f′(x) = and f′′(x) = , find all possible

x2 x3 x4

intercepts, asymptotes, relative extrema (both x and y values),
intervals of increase or decrease,

concavity and inflection points (both x and y values). Use these to sketch the graph of f(x) = 20(x − 2)

.

x2

Answer #1

1.) Use the second derivative test to find the relative extrema
for f(x) = x4 – x3 - (1/2)x2 + 11. Also find all inflection points,
discuss the concavity of the graph and sketch the graph.

Consider the function f(x) = −x3 + 4x2 + 7x + 1.
(a) Use the first and second derivative tests to determine the
intervals of increase and decrease, the
local maxima and minima, the intervals of concavity, and the
points of inflection.
(b) Use your work in part (a) to compute a suitable table of
x-values and corresponding y-values and carefully sketch the graph
of the function f(x). In your graph, make sure to indicate any
local extrema and any...

Let f (x) = −x^4− 4x^3. (i) Find the intervals of
increase/decrease of f . (ii) Find the local extrema of f (values
and locations). (iii) Determine the intervals of concavity. (iv)
Find the location of the inflection points of f. (v) Sketch the
graph of f

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

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)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.

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.
.

(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

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.

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

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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