1. Use the derivative function, f'(x)f′(x), to determine where
the function
f(x)=−2x^2+14x−8
is increasing.
2.Use the derivative function f'(x)f′(x) to determine where the
function f(x)=2x^3−27x^2+108x+13 is increasing.
3.Use the derivative function f'(x)f′(x) to determine where the
function f(x)=2x^3−27x^2+108x−12 is decreasing.
4.Find each value of the function f(x)=−x^3+12x+9 where the line
tangent to the graph is horizontal.
x=
Write f(x)=x^4+2x^3+2x+1 as a product of irreducible
polynomials, considered as a polynomial in Z3[x], Z5[x], and Z7[x],
respectively.
1. 2. Let f(x) be as in the previous exercise. Choose D among
the polynomial rings in that exercise, so that the factor ring
D/〈f(├ x)〉┤i becomes a field. Find the inverse of x+〈f├ (x)〉┤i in
this field.
For the following exercises, determine whether or not the given function f is continuous everywhere. If it is continuous everywhere it is defined, state for what range it is continuous. If it is discontinuous, state where it is discontinuous.f(x) = 2x + 5/x
Given the following rational function:
F(X)
= (2X^2 - 20) / [( X - 5 )^2]
Find all horizontal and vertical asymptotes
Find the first derivative of F(X) and
simplify
Find the critical values for X and determine if they are
at a maximum or minimum, using the First Derivative Sign
Test.
Find the Second Derivative and Use it to confirm your
answers to part c. You may keep the 2nd derivative in “rough” form
and simply substitute in the...
Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2 − 1)2 and f 00(x) =
2(3x 2 + 1) (x 2 − 1)3 . (a) [2 marks] Find the x-intercept and the
y-intercept of f, if any. (b) [3 marks] Find the horizontal and
vertical asymptotes for the graph of y = f(x). (c) [4 marks]
Determine the intervals where f is increasing, decreasing, and find
the point(s) of relative extrema, if any....
6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f
″(x) - Determine any symmetry - Find the x- and y-intercepts - Use
lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior -
Locate any vertical asymptotes - Locate any horizontal asymptotes -
Find all intervals where f (x) is increasing and decreasing - Find
the open intervals where f (x) is concave up or concave down
Please solve all if possible..
1. Determine the intervals where the function f(x)=2x^2−14x^4 is
increasing and decreasing, and also both coordinates of all local
extrema, if any. Label each extremum as a maximum or a minimum.
2. Find the absolute maximum and absolute minimum value of the
function.
f(x)=2e^x^3 on [−2,1].
3. Let f(x)=1−x^(1/3).
Determine where the graph of the function is concave upward and
concave downward, and the inflection points, if any.
Determine where the given function is concave up and where it is
concave down.
f(x)= 2x^3-6x^2-90x
Find the maximum profit and the number of units that must be
produced and sold in order to yield the maximum profit. Assume
that revenue, R(x), and cost, C(x), of producing x units are in
dollars
R(x)=50x-0.1^2, C(x)=4x+10
Find the number of units that must be produced and sold in order
to yield the maximum profit, given the equations below for revenue
and cost....
5. Consider the function f(x) = -x^3 + 2x^2 + 2.
(a) Find the domain of the function and all its x and y
intercepts.
(b) Is the function even or odd or neither?
(c) Find the critical points, all local extreme values of f, and
the intervals on which f is increasing or decreasing.
(d) Find the intervals where f is concave up or concave down and
all inflection points.
(e) Use the information you have found to sketch...