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Show that the maximum value of f(x) = x+...

Show that the maximum value of `f(x) = x+1/x` is less than its minimum value.

Text Solution

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Here, `f(x) = x+1/x`
`=>f'(x) = 1-1/x^2`
For minimum and maximum value, `f'(x) ` should be `0`.
`:. 1-1/x^2 = 0`
`=>x^2 = 1`
`=>x = +-1`
So, at `x = 1 and x = -1`, `f(x)` will be maximum or minimum.
Now, `f''(x) = 0-(-2/x^3) = 2/x^3`
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