Question

given P(x)= 2(x-1)(x+1)^2(x+2) answer the following a) what is the leading term of P(x) b) what is the degree of p(x) c) as x approaches infinity, the function P(x) _____ d) as x approaches negative infinity, the function P(x)______ e) how many turning points does it have? f) what are the coordinates of the x intercepts? g) find the coordinates of the P intercepts

Answer #1

Given f(x) = x4 – 4x3, graph the nonlinear
function and answer the following:
a) What coordinates are the absolute minimum?
b) The function is concave downward for
c) The function is increasing for what values of X?
d) What are the X- intercepts?
e) What coordinates are the inflection point?

11) Let p(x) = (4x^2-9)/(4x^2-25)
(a) What is the domain of the function p(x)?
(b) Find all x- and y-intercepts.
(c) Is function p(x) an even or odd function?
(d) Find all asymptotes.
(e) Find all open intervals on which p is increasing or
decreasing.
(f) Find all critical number(s) and classify them into local
max. or local min..
(g) Sketch the graph of p. [Please clearly indicate all the
information that you have found in (a)–(f) above.]

Given the polynomial function f (x) = (x + 3)(x + 2)(x −1)
(a) Write all intercepts as ordered pairs
(b) Find the degree of f to determine end behavior (c) Graph the
function. Label all intercepts

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 :)

Let X be a random variable with probability mass function
P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6
(a) Find a function g such that E[g(X)]=1/3 ln(2) + 1/6 ln(5).
You answer should give at least the values g(k) for all possible
values of k of X, but you can also specify g on a larger set if
possible.
(b) Let t be some real number. Find a function g such that
E[g(X)] =1/2 e^t + 2/3 e^(2t) + 5/6 e^(5t)

(a) Show that the function f(x)=x^x is increasing on (e^(-1),
infinity)
(b) Let f(x) be as in part (a). If g is the inverse function to
f, i.e. f and g satisfy the relation x=g(y) if y=f(x). Find the
limit lim(y-->infinity) {g(y)ln(ln(y))} / ln(y). (Hint :
L'Hopital's rule)

The polynomial of degree 5, P(x), has leading coefficient 1, has
roots of multiplicity 2 at x=5 and x=0, and a root of multiplicity
1 at x=−1.
Find a possible formula for P(x).

1. find all vertical asymptotes of function f(x) =
In((e^2In(x))-5x+6)
2. find all x intercepts of the function
g(x)=In((e^2In(x))-3x+5)-In(2)-In(3/2)

the global maximum of the function h(x)=1/x^2 + 1 defined on
(-infinity, infinity) is: a) 1 b) 0 c) 1/2 d) DNE
Consider a family of functions f(x)=e^-ax + e^ax for a does not
= 0. which of the following holds for every member of the
family?
a) f is always increasing b) f is always concave up c) f has no
critical points

1. Calculate the total diﬀerential for the given function.
G(x,y) = e^5x ·ln(xy + 1)
2. Apply the Second Derivative Test to the given function and
determine as many local maximum, local minimum, and saddle points
as the test will allow.
F(x,y) = y^4 −7y^2 + 16 + x^2 + 2xy

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