Calculus : Please show ALL work

5. (.5 point) Observe that f (x) : 3:1:5 8 is continuous everywhere and f (1) = 5, is negative while f (2) = 80, is positive. Therefore, by the Intermediate Value Theorem, f (9:) must have a root between 1 and 2. Use Newton's Method to estimate that root. Start with $1 = 1, and nd 373. Round your answer to three decimal places. (a) x3 x 1.714 (b) :53 = 1.5 (0) 113 % 0.038 (d) 133 m 1.462 (e) 5103 x 1.278 f(a:) : 3x5 8m 6. (.5 point) Suppose the demand function (price charged if :13 items are sold) for a certain product is given by the function 19(33) = 1000 20:12. Find the number of products that need to be sold in order to maximize the revenue. 7. (.5 point) Consider the function: f(L') = 2m3 9132 + 1216 + 7 Let M be the absolute maximum value of the function on the interval [0, 3]. Let m be the absolute minimum value of the function on the interval [0,3]. FindMm (a) Mm=7 (b) Mm=12 (c) Mm=11 (d) Mm=16 (e) Mm=9 10. (1.5 points) Consider the function f (at) = 237: (a) (0.2 point) Explain Why the function f does not satisfy the conditions for the Mean Value Theorem on the interval [0, 4] (b) (0.5 point) Show that the function f does satisfy the conditions for the Mean Value Theorem on the interval [0, 3]. (c) (0.8 point) Find the value c guaranteed by the Mean Value Theorem on the interval [0, 3]