Question

find maximum and minimum value of x+1/x​

Answer 1

Answer:

Case1. Let the x is positive number

apply AM>=GM on x and 1/x

then corresponding AM=(X+1/X)/2 , GM=1

Since X+1/X>=2

Hence Max(x+1/x)= infinity( large positive number) and Min(x+1/x)=2

Case2.Let the x is negative number

apply the same concept AM>=GM on ( -X) and (-1/X)

As we know AM &GM apply only on positive numbers

then corresponding AM=(-X-1/X)/2 , GM=1

so X+1/X<=-2

Hence Max(x+1/x)=-2 and Min(x+1/x)=-infinity ( means an very large negative number)

Conclusion: The given function varies from [-infinity,-2] &[2, infinity]

About derivative method: Actually the given function is discontinuous at X=0 so we can not apply derivative method . but if we consider the particular region except X=0 then we can still apply derivative method.

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