EXAM 2-solutions.pdf - Version 098 EXAM 2 spice(52890 1 This print-out should have 18 questions on the interval 2 Multiple-choice questions may continue

Version 098 – EXAM 2 – spice – (52890) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 00110.0pointsFind the absolute minimum value offonthe intervalbracketleftbigg12,2bracketrightbiggwhenf(x) =x2+2x-1. 1.none of the other answers2.abs. min. value = 2correct 3.abs. min. value =52 on the interval bracketleftbigg 1 2 , 2 bracketrightbigg . 00210.0pointsLetfbe a twice-differentiable function on(-∞,∞) such that the equationf(x) = 0has exactly 3 real roots, all distinct. Considerthe following possibilities:A. the equationf′(x) = 0 has at least 1 root.Which of these properties willfhave?

Version 098 – EXAM 2 – spice – (52890) 2 and 2 4 6 - 2 - 4 - 6 2 4 6 - 2 - 4 - 6 From these and the MVT we thus see that A. True: apply MVT to roots of f ( x ) = 0. B. True: by MVT f has at least two critical points. Apply MVT to these. 003 10.0points The height of a triangle is increasing at a rate of 5 cm/min while its area is increasing at a rate of 3 sq. cms/min. At what speed is the base of the triangle changing when the height of the triangle is 3 cms and its area is 9 sq. cms? Thus by the Product Rule, dA dt = 1 2 parenleftBig b dh dt + h db dt parenrightBig , and so db dt = 1 h parenleftBig 2 dA dt - b dh dt parenrightBig = 2 h parenleftBig dA dt - A h dh dt parenrightBig , since b = 2 A/h . Thus, when dh dt = 5 , and dA dt = 3 , we see that db dt = 2 h parenleftBig 3 - 5 A h parenrightBig cms/min . Consequently, at the moment when h = 3 and A = 9 , the base length is changing at a speed = 8 cms/min (recall: speed is non-negative). 004 10.0points