Completed quickly and followed instructions given. Grammar, spelling, etc. was all good as well. Thank you so much! Will hire in the future.

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(2*t*), [0, *π*/2]

absolute minimum( ) absolute maximum( )

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

*f*(*t*) = 3*t* + 3 cot(*t*/2), [*π*/4, 7*π*/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^(*−*x*2/72), [−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(2*x*) [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 *x*1 = 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 *x*1 = 0.6 as the initial approximation.

*x* = ( )

(c) Solve the equation in part (a) using *x*1 = 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*(7*π*/2) = 0

*f*(*x*) = ( )

21. Find *f*.

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

*f*(*t*) = ( )

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