Question

Consider the function f(x) =
5x^{5}+x^{4}+x^{3}+5x^{2}-x+2

What are all the possible zeroes of this function?

Find a zero of this function.

Answer #1

find all the possible rational zero
f(x) =x4 -6x3-5x2-12x-14

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

Consider the power series f(x) =x + x2/2 +
x3/3 + x4/4 +···
(a) What is the interval of convergence of this series?
(b) Differentiate this series term by term and compare the
result to one of the series that we found in the lecture to find
the closed form of the series f(x).

2.
Consider the following function.
f(x) =
x2 + 9
if x ≤ 1
5x2 − 1
if x > 1
Find each value. (If an answer does not exist, enter DNE.)
f(1)=
lim x→1− f(x)
=
lim x→1+ f(x)
=
Determine whether the function is continuous or discontinuous at
x = 1.
Examine the three conditions in the definition of
continuity.
The function is continuous at x = 1.?
or
The function is discontinuous at x = 1. ?

Consider the function f(x)=x4 e-3xShow all
work for the following problems.
(5a) (3pts) Find all critical numbers of
f(x)
(5b) (4pts) On what intervals is f(x)
increasing/decreasing? (State the intervals clearly, and show
associated mathematical work)
(5c) (3pts) Find all local maximum and local
minimum values of f(x)

Consider a function f(x; y) =
2x2y
x4 + y2 .
(a) Find lim
(x;y)!(1;1)
f(x; y).
(b) Find an equation of the level curve to f(x; y) that passes
through the point (1; 1).
(c) Show that f(x; y) has no limits as (x; y) approaches (0;
0).

Approximate the zero for f(x) = (x^3)+(4x^2)-3x-8 using newton's
method
Use x1 = -6
A)Find x2,x3,x4,x5,x6
B)Based on the result, you estimate the zero for the function to
be......?
C)Explain why choosing x1 = -3 would have been a bad idea?
D) Are there any other bad ideas that someone could have chosen
for x1?

1. (Continued) Consider the function
(e)
(f)
f (x) = x3 − 7 x + 5. 2
(0.5 pt) Find the possible inflection points of f(x). Show
work.
(0.5 pt) Test the possible inflection points of f(x) to
determine if each point is or is not an inflection point. Your work
must show that you tested each point properly and support your
conclusion. Be sure to state your conclusion. Show work.
(g)
(1 pt) Find the global minimum and global...

Determine all the zeroes of f(x) and sketch a graph of the
function including accurate intercepts.
f(x)=2x5-9x4+28x3-84x2+90x-27

(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

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