Question
Asked Nov 10, 2019
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Draw 1st & 2nd derivative charts. Identify extrema & inflectionn points.

y = x2 + 2/x

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Expert Answer

Step 1

Consider the function,

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2 y = x Since y x2is not defined at x = 0.Domain of y is x < 0 or x> 0 х Differentiate y = x +=, we get dx 2 y2x To find critical point set y 0, we get 2 2х- 0 x =1 Therefore the critical point is 1.Combine critical point with the domain, we get the intervals x<0,0 x<1,1 <x<o.

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Step 2
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Now find the nature of y as follows Interval 2 y = 2x 2 х The function is decreasing 2 =-4 < 0 y() 2) 2 on (0,0) (-1) The function is decreasing on (0,1) 0<xl 2 y (0.5) 2(0.5) (0.5) 2 The function is increasing 2 >0 y (2) 2(2) (2) on (10) From table, the function y is decreasing on (0,1) which implies y does not have maximum and the minimum occurs at x =1

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Step 3
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To find minimum substitute x=1 in y 2 y12 1 = 3 Therefore, y has no maximum and the minimum occurs at(1,3)

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