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Question

The function f(x)= x1x2,(x>0) has
  1. A local maxima
  2. A local minima
  3. Neither a local maxima nor a local minima
  4. None of these


Solution

The correct option is A A local maxima
Let f(x)=x1x2
f(x)=12x21x2=0x=±12
But as x > 0, we have x=12
Now, again f′′(x)=1x2(4x)(12x2)x1x2(1x2)
=2x33x(1x2)3/2
f"(12)=ve. Then f(x)is maximum at x=12

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