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+1
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avatar+62 

x+4/x2

Can someone show how they get a minimum turning point of (2,3) and it has no points of inflextion 

Thank you so much 

 
Ashreeta  Dec 6, 2017
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1+0 Answers

 #1
avatar+79819 
+2

y  =  x  + 4/x^2

 

Write as

 

y  = x  + 4x^(-2)

 

y ' =  1  - 8x^(-3)        

 

Set this  = 0

 

1 -  8x^(-3)  = 0  

 

1  =  8 / x^3  multiply both sides by x^3

 

x^3  = 8    ⇒    x  = 2

 

 

And when  x  = 2,  y  =  2 + 4 /(2)^2   =   2  + 1   = 3

 

Take the second deriviative

 

y''  =  24x^(-4)  =  24 / x^4

 

Putting 2 into this gives a positive.....so....this indicates that (2,3)  is a minimum

 

Here"s the graph : https://www.desmos.com/calculator/3xcrgvdoyl

 

 

cool cool cool

 
CPhill  Dec 6, 2017

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