SOLUTION: What is the least possible value of X^2-1/X^2 If x>=1

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Question 1143083: What is the least possible value of X^2-1/X^2 If x>=1
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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Take the derivative 


    2x - %28-2%29%2Fx%5E3 = 2x + 2%2Fx%5E3.


In the domain x >= 1  the derivative is always positive -- so, the function monotonically grows at x >= 1.


Therefore, the minimum of the function in this domain achieves at x = 1 and is equal to

    1%5E2 - 1%2F1%5E2 = 1 - 1 = 0.



The last step in solving such exercises is to make a plot


    graph%28+330%2C+330%2C+-5%2C+5%2C+-20%2C+20%2C%0D%0A++++++++++x%5E2+-+1%2Fx%5E2%0D%0A%29

            Plot y = x%5E2 - 1%2Fx%5E2


to make sure (visually) that our conclusions are correct.