Sol#12 - MATH 171-10c Assignment 12 Guidelines Begin by...

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Unformatted text preview: MATH 171-10c, Assignment 12 Guidelines Begin by answering the questions in the space provided; you may write on both sides of the paper. Additional sheets may be attached if necessary. Staple all sheets together before submission. Put down the names of all group members in the top right corner. Write neatly and legibly; untidy presentation may lead to appropriate penalization. Due: Friday, April 23rd 1. (15 marks) Prove that the following pair of inequalities holds for every :1: 2 0: 1—2xge”2zgl——2z+2m2 2. (10 marks) Suppose that the function f is twice continuously differentiable in the open interval I, and that f” >_ 0.for every :1: in I. Prove that the graph of the function C(95) = em), a: e I, is concave up in I. 3. (10 marks) Let N be a fixed (but arbitrary) positive integer. Consider the polynomial N P(a;) = Z‘akzzk, —-00 < :1: < 00, 16:0 where ak > 0 for every 0 S k S N. Use Question 2 above to show that the graph of the 3 function g h(a:) = em”), —00 < a: < 00, is concave up in (—00, oo). X:f: M NM- __* “w M w , ,, , _ _ v - - - ~51 - _ '92.?“ -- .. 1 )c A \ .. a.“ r .. i) Let: 1: 5 “l'i‘flx, X 7’0. m) Fox)‘ at: +1 20 a )) x36 a l' ‘° , AS {E‘ ¢¢wb§nmaw~s N we y 7, o) flew. a M '3: l ) 5 ° F 2" Q \J x a“ a a ,_ . 0 l V F Mwst Won Atcvita‘rSiha ‘1‘ La! W3} \h(0 03’) “WA l“ (7020 V¥~>OZ I r xvii.“ Mgvxw W I TLC ’ R’wvas tin?— ‘lznivsl: ‘fiL‘lIk A. ‘Wé . 3 \ 1‘6 1 «1x 5'13 Week: N (4 ‘F ) 1m " Mu k3) 0‘ 1 Z 6‘1 =9 3‘05); 2 “((142) x. " o E; ' N H ‘mh»' w = lawman) x {a} .V ' -' kJL ’ = ZQRMHW"): », lk‘l .. . - -' u- ' ' was}. V NM; mayo) @&)(kax))q) «35$. 7. v,a week. g9 13'“ 7; 10“ P '0 ‘ V,‘ ‘ Nafié “H”; 13% “my-5w? "€Wm QM-s-k-C‘gag. '51., ’ ' ...
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Sol#12 - MATH 171-10c Assignment 12 Guidelines Begin by...

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