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Unformatted text preview: y (300y 2 ) subject to < y < √ 300 . If f = y (300y 2 ) = 300 yy 3 , then df dy = 3003 y 2 . The maximum occurs when y = 10 and consequently x = 200 . Q8 (a) increasing everywhere, (b) One critical point at x = 1 , f (1) = 1ln(2) , type other. No local extrema. (c) x = 1 is a point of inﬂection, i.e. (1 , 1ln(2)) in the xyplane. x =1 is another point of inﬂection i.e. (1 ,1ln(2)) in the xyplane. (d) Sketch and details below. > f:=x  ln(1+xˆ2); f := xln(1 + x 2 ) > g:=diff(f,x); g := 12 x 1 + x 2 1 > g:=factor(g); g := (1 + x ) 2 1 + x 2 > solve(g,x); 1 , 1 > h:=diff(g,x); h :=2 1 + x 2 + 4 x 2 (1 + x 2 ) 2 > h:=factor(h); h := 2(1 + x )(1 + x ) (1 + x 2 ) 2 > solve(h,x); 1 ,1 > plot(f,x=2. .4); –3 –2 –1 1 –2 –1 1 2 3 4 x 2...
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 Fall '10
 Drury
 Calculus, Continuous function, lim x→1− x→1+

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