1. (10 points) Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 441 square meters, show your work. (a) square base side 25 ; height Ly (b) square base side Ze ; height Ly (c) square base side Zo ; height Ive (d) square base side " ; height Ive (e) square base side LY" ; height 17vi 2. (10 points) If the total cost function for a product is C(r) = 400 + 9r + 0.01r- dollars, determine how many units x should be produced to minimize the average cost per unit, show your work. (a) 450 units (b) 400 units (c) 141 units (d) 200 units (e) 97 per unit 7. (10 points) Use the limit definition lim f(x + h) - f(x) h -H h to show that the derivative of the function /(x) = 12 - 1 is 2r, show your work.8. (7 points) Find the limit if it exists, show your work. r' - 20- 8 lim C+2 (a) 1 (b) 0 (c) -1 (d) none of the above 9. (7 points) Find the constant a such that the function is continuous on the entire real number line, show your work: if Arta if (a) DNE (b) 0 (c) 1 (d) none of the above10. (18 points) Suppose that f(x) = x2 + 1 on the closed interval [-4, 4), show your work. If you are unsure how to solve the above equation, (15 points) f(x) = -23 + 3x - 7 (a) Find f'(x) (b) Find the critical numbers (c) Find absolute maximum and minimum and local maximum and minimum. (d) Determine the open intervals when f is increasing and when f is decreasing(e) Does f have any inflection points? If so, state them below. (f) Determine the open interval where f is concave up and concave down 1. (5 points) Extra credit Find the open interval where f(x) increases and decreases using the First Deriva- tive Test of f(x) = 1$(6 -x), show your work 2. (5 points) Extra Credit Graph the faction f(x) = ri(6 -x)i using the first and the second derivative test, show your work. SCORE / 115