Question

Given f(x) = 2x^{3} − 7x^{2} – 3x + 8

a) Find all roots of the function and simplify them as much as possible

b) Sketch the complete graph

c) indicate the viewing window

d) Find the x-intercepts

e) Find the relative maximum and minimum to the nearest hundredth

Answer #1

(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

Given f(x)=2x3-7x2+9x-3, use the remainder theorem to
find f(-1)

Let f(x)= 3x^2-6x+1. Express this quadratic function in the
standard form . Find the vertex, the minimum or maximum value of
function , x-intercepts, y-intercept, domain and range. Show your
table of values, and sketch the graph.

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

given that f'(x)=-3x^2 -6x answer the following
what inteeval is f(x) increasing or decreasinf
find x coordinates of all inflection points of f(x)
on what interval is f(x) concave up and down
suppose (-2,0), (1,0) and (0,4) are intercepts of f(x) whose
domain is all real. sketch a possible graph of f(x)
find f(x) by integrating f'(x) and intercept information from
above
find all global extrema on interval [-1,5]
show work please and thanks in advance :)

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.

1. You are given the function f(x) = x/(1−x)
a) Find the x and y- intercepts.
b) Find the horizontal asymptote(s).
c) Find the vertical asymptote(s) and do a limit analysis of the
behavior of f on either
side of each vertical asymptote.
d) Find the critical number(s) of f.
e) Find the interval(s) of increase and decrease of f.
f) Find the relative maximum and minimum value(s) of f.
g) Find the hypercritical number(s) of f.
h) Find the...

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

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

1) The function f(x)=2x3−33x2+108x+3f(x)=2x3-33x2+108x+3 has one
local minimum and one local maximum. Use a graph of the function to
estimate these local extrema.
This function has a local minimum at x
= with output value =
and a local maximum at x = with output
value =
2) The function f(x)=2x3−24x2+42x+7 has one local minimum and
one local maximum. Use a graph of the function to estimate these
local extrema.
This function has a local minimum at x
= with output value =...

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