MAT301 Exam #2 DO ANY NUMBER OF PROBLEMS THAT TOTAL 75 POINTS IF NECESSARY, YOU CAN REDUCE (NOT INCREASE) THE VALUE OF ANY ONE PROBLEM (EXCLUDING THE 75 POINTS QUESTION) TO ENABLE YOU TO TOTAL 75 POINTS

MAT301 Exam #2 DO ANY NUMBER OF PROBLEMS THAT TOTAL 75 POINTS IF NECESSARY, YOU CAN REDUCE (NOT INCREASE) THE VALUE OF ANY ONE PROBLEM (EXCLUDING THE 75 POINTS QUESTION) TO ENABLE YOU TO TOTAL 75 POINTS YOU MUST SHOW ALL WORK TO RECEIVE FULL CREDIT 1) In this problem,let x = 2! the value Ax = dx, dy = f(X)dx, and A}! = f(x + Ax ) _ f0") to complete the table f(x) = '5' 20 POINTS dx = Ax 0y Ay Ay dy dy A7 1.0000 0.5000 0.1000 0.0100 0.0010 5x x) = i 2) Find the rst derivative given that 24" + 3 15 POINTS 01/ 3) Find 03! by implicit differentiation. 11" + y + VXY = 4 20 POINTS 4) A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is owing into the tank at the rate of 10 cubic feet per minute, nd the rate of change of the depth of the water the instant it is 8 feet deep? 1 = - arr2 h 3 15 POINTS 5) Locate the absolute extrema of the given function (if any exist) over the indicated interval. {(x) = 3x2 +6x-2 a) [-1i4] 1)) [-1,4) 0) (-1,4] d) (-134) 15 POINTS 6) Determine if Rolle's Theorem can be applied. If Rolle's Theorem can be 1" applied, nd all values of c in the interval such that f (C) = 0 f(x) = (x + 3)(x + 2)2 closed interval [-3, 2] 15 POINTS 7) Apply the Mean Value Theorem to f on the indicated interval. Find all values fb fa ofcinthe interval [(3, 1)] such that b a f(x)=3x_5 25x54 "+1 20 POINTS 8) Sketch the graph of the given function. Make use of intercepts, relative extrema, points of inection, domain, range and asymptotes. You must include the 13 steps with headings as shown in your notes as well as in the YouTube video in order to be credited for this question. Show all work including how you found your derivatives. f (x) = (xil), T5 POINTS 9) An open box is to be made from a square piece of material, 12 inches by 12 inches, by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume. 20 POINTS H 'lE-EH s 10) Find the indicated limit 2x lim( ) H" W: +1 10 POINTS