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FUNDAMENTALS OF MATHEMATICS DIFFERENTIAL CALCULUS by Sanjay Mishra

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SECTION—II
SUBJECTIVE SOLVED EXAMPLE
  1. Show that the maximum value of (1/x)x is e1/e.

    Solution:

    image

    Then logy = x log(1/x) = – x log x

    Differentiating both sides with respect to x, we get

    image

    Differentiating again with respect to x, we get

    image

    From (ii), image

    images

    For maximum ...

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