Consider the function ?(?)=(?^(4/5))*(?−3). This function has two critical numbers ?<?

1) Then ?= ? and ? = ?.

2) For each of the following intervals, tell whether ?(?) is increasing or decreasing.
(−∞,?]:   ?
[?,?]: ?
[?,∞): ?

3) The critical number A is ? and the critical number B is ? (a relative maximum / a relative minimum / neither max nor min )
There are two numbers ?<? where either ?″(?)=0 or f″(x) is undefined.

4) Then C = ? and D = ?

5)Finally for each of the following intervals, tell whether ?(?) is concave up or concave down.
(−∞,?): ?
(?,?): ?
(?,∞): ?

Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The point (0, 0) is a stationary point of f. For what values of k will f have a local minimum at (0, 0)?

(a) |k| > 4

(b) k ≥ −4

(c) k ≤ 4

(d) |k| < 4

(e) none of the above

The point P : (2, 2) is a stationary point of the function f(x, y) = 6xy − x ^3 − y^ 3 . f has (a) a local maximum at P (b) a local minimum at P (c) a saddle point at P (d) a discontinuity at P (e) none of the above

F

Approximate the arc length of the curve over the interval using Simpson’s Rule SN with N=8.

y=7e^(−x2) on x∈[0,2]

(Use decimal notation. Give your answer to four decimal places.)

Find the general solution y(t) to the following ODE using (a) Method of Undetermined Coefficients AND (b) Variation of Parameters:

2y"-y'+5y = cos(t) - e^t Sin(t)

Consider the equation: x² y''-6y=0

A. Could you solve this ODE using Homogeneous Linear Equations with Constant Coefficients? Explain.

B. Note that y₁=x^₃ is a solution of the ODE. Using reduction of order, find a solution y₂ such that { y₁, y₂} is linearly independent.

C. Prove that{y₁, y₂} is linearly independent.

D.What is the general solution?

Find the area of the region enclosed by the graphs of y^2 = x + 4 and y^2 = 6 − x

A projectile is launched at a height of 5ft. On the ground with an initial speed of 1000 feet per second and an angle of 60 with the horizontal. Use the movement of a projectile that does not consider air resistance and determines:

The vector function that describes the position of the projectile
The parametric equations that describe the motion

The time it took for the projectile to go up

The maximum height

The time of flight

The maximum horizontal range of the projectile

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 2y cos(x),    0 ≤ x ≤ 2π

The function H(t)=16t^2 + 64t gives the height (in feet) of a golf ball after t seconds.

a)Determine the maximum height of the golf ball.

b) How long does it take for the ball to hit the ground?

c)Identify the vertical intercept. Write the answer as an ordered pair.

d)Determine the practical domain of H(t).

e)Determine the practical range of H(t).

equation for part A ?(?) = −0.48?^2 + 7.2? + 63

equation for part B ?(?) = −?^2 + 8? + 84

the Georgia marching band discovers that the amount of time it spends playing “Glory, Glory to Old Georgia” has a direct impact on the number of points Georgia’s team scores. If the band plays for x minutes, then the Bulldogs will score ?(?) = −0.48?^2 + 7.2? + 63. points in the game. Assume the band can play for a maximum of 10 minutes

. a. How long should the band play to maximize the number of points Georgia scores? Show your work and explain.

b. The band affects how many points Tennessee scores as well. When the UGA band plays for x minutes the Volunteers score ?(?) = −?^2 + 8? + 84. points in the game. Find the number of minutes the band should play to maximize the margin of victory for Georgia (i.e., the points by which Georgia wins). Again, please show all work. [Hint: You should use both V (x) and B(x).]

c. What will be the score of the game you found in part (b)?

For the following differential equation

y'' + 9y = sec3x,

(a) Find the general solution y_h, for the corresponding homogeneous ODE.

(b) Use the variation of parameters to find the particular solution y_p.

For each of these differential equations with initial conditions compute the first five terms in the series solution centered at the given point. 1. y 0 = y − x, y(1) = 2 centered at a = 1 2. y 00 = 2y 0 − y, y(0) = 3, y0 (0) = 1, centered at a = 0

The temperature at a point (x,y,z) is given by T(x,y,z)=200e^(-x^2-y^2/4-z^2/9) , where T is measured in degrees Celsius and x,y, and z in meters. just try to keep track of what needs to be a unit vector. a) Find the rate of change of the temperature at the point (1, 1, -1) in the direction toward the point (-5, -4, -3). b) In which direction (unit vector) does the temperature increase the fastest at (1, 1, -1)? c) What is the maximum rate of increase of T at (1, 1, -1)?

1. Identify and explain the advantages and disadvantages of virtual teams. Outline the factors required for virtual teams to be successful.

2. Describe the kinds of behaviours that individual team members can engage in that positively impact overall team effectiveness.

3. Describe the kinds of behaviours that individual team members can engage in that negatively impact overall team effectiveness.

4. Outline how you intend to approach participation in your group project, explaining how your plans for participation will likely impact your project team. Include an analysis of your results from the Group/Team Skills activity you completed from the Module 6 reading.

This is Canadian Organizational Questions