Help with explanations and steps if u have to please

("1. Use the chain rule to nd the_'der'ivaiives of the following: a. {3 pts) yE (2x3 5:02. you no nor HAVE TO SlMPLl'FY. b. (3 pts) y = 3(.:t2 + 20*. you no NOT HAVE TO SIMPLIFY. 4 (3 pts) y = i ). YOU DO NOT HAVE TO SEMPLEFY 5x AN Y ARROWS BELOW INDICATE GOING TO INFINITY OR TO NEGATIVE INFINITY. 2. HJOXUI-h-PJ 8. 9. Given the picture do these: a. (4 pts) Give 4 critical numbers. b (2 pts) Give 2 relative maxes. c. (2 pts) Give 2 relative ruins. d. (2 pts) Give all labeled points of inection. e f. g (2 pts) Are there any absolute ruins? If so, give them. If none, why not? (2 pts) Are there any absolute maxes? If so, give them. If none, why not? (2 pts) Give any points (x, y) where the Function is concave down. h. (2 pts) Give any points (x, y) where the anction is concave up. (3 pts) For f(x) = I2 above, find the x value where the derivative f '(x) = 16. SHOW SOME WORK. (3 pts) Draw a polynomial function with max = 2 and always concave down. {3 pts) Draw a Function with an absolute min of 1 and is n_0r differentiable at that min. (3 pts) Draw a inction of x that is not continuous at x = 3 and has a max of 3. Given f(x) = 2x2 +1296 + 2, do these: a. (5 pts) Find all points (x, y) where the derivative is 0. b. (3 pts) Find the 2"d derivative and tell what it shows about the function. (6 pts) Given f (x) = x'1 4.1:3 20x2 3, nd any critical numbers. Just X coordinates. Given f(x) = x3 + 6x2 + 9x + 1 do the following: a. (5 pts) Find the x values where the derivative is '0. b. (3 pts) Use f " to give the concavity (up or down) for your 3: numbers in part a. c. (3 pts) Find any points of inection (x, y) of this function. 10. Given 2x2 + y3 = 2x + 8, do this: HINT: USE THE 3 RULES a. (5 pts) Use implicit differentiation to nd y' or dytdx if you prefer. b. (3 pts) Plug the point (1, 2) into your y' or dytdx for part a, and nd the slope of the tangent line. 11. (5 pts) Given xzy + y2 = x3 + 2,nc1 y' or dytdx by implicit differentiation. HINT: See a product rule? 12. 5 pts) You have 48 feet of fence and want to make a rectangular corral (as big as possible} divided into 3 rectangular corrals as in the picture. NO RIVER! Find the length and width of the big rectangle. LABEL ANSWER. ECU 13. A bus on a straight road moves according to the equation SO) = 3 12! where t is time in hours and 5(1) is the position of the bus' in miles. Do these: _ a. (2 pts) Find the position of the bus after 3 hours. LABEL ANSWER AS MILES. b. [4 pts} Find when the bus is not moving (Le. velocity = 0 miles per hour). LABEL ANSWER IN HOURS. NEGATIVE ANSWERS ARE OKAY. c. [3 pts) I Find the acceleration of the bus at t= 2. LABEL IT AS MILES PER HOUR PER HOUR. 14. (4 pts) An open-top box is to be madc from a square piece of cardboard that is 8 inches on a side by cutting a square from each corner and folding up the sides. Set up the equation to nd the box of biggest volume. DO NOT SOLVE. 15. (5 pts) A square iece of metal has area A = x2 . It is being heated u , and each side it is increasing in size at a speed of l3 P dx d/l ' E = 2 inches per hour. Find when each side is 14 inches. LABEL ANSWER. Hint: Use chain rule. J4