1. Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = ((x^2) − 1)^3, [−1, 4]

absolute minimum( ) absolute maximum( )

2. Find the absolute maximum and absolute minimum values of f on the given interval.

f(t) = 2 cos(t) + sin(2t), [0, π/2]

absolute minimum( ) absolute maximum( )

3. Find the absolute minimum and absolute maximum values of f on the given interval.

f(t) = 3t + 3 cot(t/2), [π/4, 7π/4]

absolute minimum( ) absolute maximum( )

4. Find the absolute maximum and absolute minimum values of f on the given interval.

f(t) =t*sqrt (64-t^2) [−1, 8]

absolute minimum( ) absolute maximum( )

5. Find the absolute maximum and absolute minimum values of f on the given interval.

f(x) = xe^(−x2/72), [−5, 12]

absolute minimum( ) absolute maximum( )

6. Find the absolute minimum and absolute maximum values of f on the given interval.

f(x) = x − ln(2x) [1/2 , 2]

absolute minimum( ) absolute maximum( )

7. Find the dimensions of a rectangle with perimeter 84 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)

( )m (smaller value)

( ) m (larger value)

8. Find the dimensions of a rectangle with area 1,000 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)

( )m (smaller value)

( ) m (larger value)

9. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil (measured in appropriate units) is

Y =KN/(9+N^2)

where k is a positive constant. What nitrogen level gives the best yield?

N=( )

10. The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function

P = 120i/(i^2 + i +4)

where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?

i= ( ) thousand foot-candles

11. Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. Find the largest volume that such a box can have.

Finish solving the problem by finding the largest volume that such a box can have.

V=( )ft^3

12. A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used.

sides of base =( )m

height =( )m

13. If 1,200 cm^2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

( )cm^3

14. (a) Use Newton’s method with x1 = 1 to find the root of the equation

x^3 − x = 4

correct to six decimal places.

x = ( )

(b) Solve the equation in part (a) using x1 = 0.6 as the initial approximation.

x = ( )

(c) Solve the equation in part (a) using x1 = 0.57. (You definitely need a programmable calculator for this part.)

x = ( )

15. Use Newton’s method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)

3 cos x = x + 1

x = ( )

16. Use Newton’s method to find all roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)

(x − 5)^2= ln(x)

x=( )

17. Use Newton’s method to find all real roots of the equation correct to six decimal places. (Enter your answers as a comma-separated list.)

8/x=1+x^3

x=( )

18. A particle is moving with the given data. Find the position of the particle.

v(t) = 1.5*sqrt(t) s(4) = 13

s(t)=( )

19. Find f.

f ”(θ) = sin(θ) + cos(θ), f(0) = 2, f ‘(0) = 3

f(θ) = ( )

20. Find f.

f ”(x) = 4 + cos(x), f(0) = −1, f(7π/2) = 0

f(x) = ( )

21. Find f.

f ”(t) = 3e^t + 8 sin(t), f(0) = 0, f(π) = 0

f(t) = ( )

Next to these stages, there are four types of loyalty. The first type is no loyalty: this can be seen as the typical action supporter that is giving money to fundraiser friends/family. There is no connection between the action supporter and War Child, non-loyal customers add a small amount to the financial account of the organization. The second type is inertia loyalty: this type can be a potential Friend, the person is giving a donation because they always have done it. This person is not loyal to one charity because there is no deeper connection and is easy with switching from charity to charity. This person is reachable to get a deeper connection with to become a potential Friend. It is needed to give the potential Friend attention and please the person. The third type is latent loyalty: this type is based on situational influences such as time, social life, physical factors, reasons why to support charity and the mood of the person. Latent loyalty means that there are repeated purchases. The last type is premium loyalty: this is the greatest type an organization can get. This type indicates the loyal Friend who is proud to discover more and tell about War Child to everyone. (Griffin, 2010) Using the stages and types of loyalty, War Child will get a better understanding about their potential Friends. Increased loyalty can give benefits to more respects of the company. Increased loyalty will be cost saving because there will be reduced marketing costs, more positive word-of-mouth, satisfied loyal customers whereby the failure costs decrease. (Griffin, 2010) 1.2.4 Customer relationship management Kotler (2014, p. 9) stated in the book ‘’Principles of marketing’’ that customer relationship management (CRM) can be mentioned as delivering superior customer value and satisfaction by building and maintaining profitable customer relationships. (Kotler, 2014) Using a suitable approach for the action supporters will lead to charitable giving. To build and maintain profitable customer relationships, customer relationship management need to be implemented. It is very important to deliver customer value and make the action supporters satisfied. By doing this,>

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