Please evaluate these question with every step and every explanation for each of one.

Lef f(x)= -(3/8)x⁴+x³+1, where x∈(−∞,∞)

1)Find the critical numbers of f(x)

2)Find the absolute maximum value and the absolute minimum value of f(x) on the closed interval [-1,3]

3)Find the intervals where f(x) is increasing and the intervals where it is decreasing. Find the local maximum values and the local minimum values of f(x)

4)Find the intervals where the graph of f(x) is concave upward and the intervals where it is concave downward. Find the inflection points of f(x)

a. Find the volume of the solid obtained by rotating the region enclosed by the curves y = 4 x^2 , y = 5 − x^2 about the line y = 11

b. Find the volume of the solid obtained by rotating the region enclosed by the graphs about the given axis.

y = 2sqt (x), y=x, about x=-20.

Please leave your answer in fraction if possble

every quadrilateral tessellates the plane. However, can an arbitrary quadrilateral such as the one shown below have all its sides altered and still tessellate the plane? Decide which methods described in this activity set you can use to alter the sides of this quadrilateral and tessellate the plane. In the pictured quadrilateral, no sides are of equal length and no sides are parallel. For each method you use, make a template for your figure, and determine whether or not it will tessellate the plane. Describe your results and include any clarifying diagrams.

Find the absolute extreme values of g(x, y) = x^2 + xy over the rectangle ? = {(?, ?) : − 2 ≤ ? ≤ 2 , −1 ≤ ? ≤ 1}

Need examples of problems and proofs being solved surrounding group cohomology

Find the determinant of A by (repeatedly) expanding on the column or row of your choice.

A =

Perform the following straightedge and compass construction. State all steps as clearly as possible
- The Orthocenter of a non regular triangle

.

You are mountain climbing with a friend. You need to reach a ledge that is 22 feet above you. You toss a grappling hook with a velocity of 32 feet per second. The equation that models the path of your hook is given by the function below:
h(t)=−16t2+32t+5

a. Write the equation in vertex form. Describe the graph by identifying the vertex, axis of symmetry, and the direction of the opening.
b. What is the maximum height you have thrown the hook?
c. What is the result of this toss?

You decide to try again and increase the velocity of your toss to 34 feet per second.
d. What is the maximum height of this toss?
e. What is the result of this toss?
f. What are the x and y intercepts? Do they have meaning in the context of this problem? Explain.
g. What is the domain in this problem? What does it represent in the problem?

Let A = (3, 4), B = (0, −5), and C = (4, −3). Find equations for the perpendicular bisectors of segments AB and BC, and coordinates for their common point K. Calculate lengths KA, KB, and KC. Why is K also on the perpendicular bisector of segment CA?

Prove Euclid's Fifth Postulate using Triangle Sum?

Part A. Find the horizontal and vertical asymptotes of ?(?)= (6x^2) / (7(x^2 + 8))

Part B.  Find the horizontal and vertical asymptotes of ?(?)= (x^2 - 3) / (x^2 + 2x - 8)

Part C. Find the horizontal and vertical asymptotes of ?(?)= (x^2 - 49) / (3x^2 - 75)

Part D. Find the horizontal and vertical asymptotes of ?(?)= (x^3 - 6) / (x^2 + 14x + 49)

Q1).The cost of a four-year private college education (after financial aid) has been estimated to be $50,000.† How large a trust fund, paying 4% compounded quarterly, must be established at a child's birth to ensure sufficient funds at age 18? (Round your answer to the nearest cent.)

Q2). Find (without using a calculator) the absolute extreme values of the function on the given interval.

f(x) = x/x^2+9 on [-5,5]

find maximum and minimum

Q3). For the function, do the following.

f(x) = 3/x from  a = 1  to  b = 2.

(a) Approximate the area under the curve from a to b by calculating a Riemann sum using 10 rectangles. Use the method described in Example 1 on page 351, rounding to three decimal places.

(b) Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the Fundamental Theorem.

The revenue R (in millions of dollars) for a company from 2003 through 2016 can be modeled by

R = 6.211t³ − 152.89t² + 990.1t − 414,    3 ≤ t ≤ 16

where t represents the year, with t = 3 corresponding to 2003.

(a) Use a graphing utility to approximate any relative extrema of the model over its domain. (Round each value to two decimal places.)

Relative maximum: (t,R)=

Relative minimum: (t,R)=

(b) Use the graphing utility to approximate the intervals on which the revenue for the company is increasing and decreasing over its domain. (Enter your answers using interval notation. Round each value to two decimal places.)

Increasing: ( )

Decreasing: ( )

(c) Use the results of parts (a) and (b) to describe the company's revenue during this time period.

For the system

2x1 − 4x2 + x3 + x4 = 0,

x1 − 2x2 + 5x4 = 0,

find some vectors v1, . . . , vk such that the solution set to this system equals span(v1, . . . , vk).