Question
Asked Nov 8, 2019
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Consider the following function:

f(x)=x^2ln(x)

a.) find the intervals on which f is increasing or decreasing

b.) find local maximum and minimum values

c.) find intervals of concavity and inflection points 

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Expert Answer

Step 1

a)

Consider the function,

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f (x) x In (x) Differentiate f (x)= x2 In (x), we get d (x2 In (x)) x(1+2 In x) To find critical point set f (x) = 0, we get x(1+2 n x)( x0,(12 n x 0 x = 0,x =e1/2 Therefore, the critical point is x = 0,x = e12. In interval notation 0, ((F»}

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Step 2
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Now find the nature of f (x) as follows For the interval 0<x<- Letx- 2 1 12 n 2 <0 2 2 1 Since f (x)0 the function is decreasing on 0, Ne

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Step 3
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1 x oo For the interval Let x 1 (1)1(1+2 In 1) =1+2(0) =1>0 1 Sincef (x)0 the function is increasing on («4) ,aoand is decreasing on 0, Therefore, f(x is increasing on

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Tagged in

Math

Calculus