Question 1 (16 points) Refer to Section 1 in the course notes Find the maximum and minimum value of f($) = Q33 6502 l 923' 4 on the interval% S (E S 5 There is a minimum value at x= '3/ The minimum value is '3/ There is a maximum value at X: The maximum value is A Question 2 7 points) Refer to Section 1 in the course note You are asked find the maximum and minimum values of y = 5133 3(32 9m + 5 on the interval 0 S {I} S 4. Determine which of the given x-values is a test value. 1. Test value 2. Not a test value x=1 x=-1 UUUQUUU Question 3 (15 points) Refer to Section 2 of the course notes A farmer would like to enclose an area by fencing in three sides alongside an existing fence and split the area into 3 parts, as shown in the picture below. The fencing for the outer part of the fence costs $16 per meter and the fencing for the inner partition costs $12 per meter. What dimensions will maximize the area and what is the maximum area that can be enclosed for $1600? aauaj Eunsixg Just enter the numbers! The length of the inner partitions and the outer side parallel to the existing fence is: S 'v meters. The length of the outer side adjacent to the existing fence is: 4/ U meters. The length of the outer side adjacent to the existing fence is: 6/ U meters. The area is: 4/ meters U Question 4 (6 points) Refer to Section 2 in the course notes You are constructing a metal can with bottom and open top with height h and radius r as shown in the picture below. The formula for the volume of the can is V = 7T7'2h and the surface area is S = 27rrh + 71'1'2 The can must hold 16 ounces with minimal surface area. Determine which are the objective and constraint equations. DO NOT SOLVE THE PROBLEM 1- V = 7rr2h \fQuestion 5 (10 points) Refer to Section 4 in the course notes A store sells 400 refrigerators per week for $600 each. A survey indicates that for each $50 rebate offered, the store will sell an additional 75 refrigerators. Match the demand function, f(x) and the revenue function, R(x) to the correct expression. 1 . y = N /CO 2 + 100x 2. U = N / CO + 1300x 3 . y = 2 + 1000 3 2C + 2600 The Demand Function, f(x) 4. y = 3 The Revenue Function, R(x) 5. V = - CO N .2 + 2600 3 6. y = 1000 CON .2 + 3 - X 7. y = 2 + 1007- yzgm+100 8- y = gm+ 1300 Question 6 (12 points) Refer to Section 4 in the course notes. 5 The demand function for a certain item is X) = _ 3X + 20. Just enter the number for each of your answers. The price that should be charged to maximize revenue is: 6/ The maximum revenue is: 6/ How many units must be sold to maximize revenue? 6/ Question 7 (12 points) Refer to Section 5 in the course notes d Use the product rule to compute Ems\" + 1X2X + 5)) by following the steps. Let f(m) = 333' + 1 and g($) = 256 + 5.Then f'(w) = :l "J and gl(.'B) = Sw Now plug in and simplify (no spaces in your answer), (f($) -g(m))' = f(m)g'(m) + 9(iv)f'(iv) = l:] v Question 8 (8 points) Refer to Section 5 in the course notes Let f (t) = 173905) where 9(t)is some unknown differentiable function. Which one is f, (t)? Question 9 (9 points) Refer to Section 6 in the course notes 2 1 Let g ($) = gin:7 . Use the quotient rule to find g(4). Round your answer to 2 decimal places. Your Answer: :]