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MHT CET202123 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

Function f ( x )= e ^ -1 / x is strictly increasing for all x where

Options

  1. Ax is only positive real number
  2. Bx is only negative real number
  3. Cx is a real number
  4. Dx is a non - zero real number

Correct answer

D. x is a non - zero real number

Step-by-step solution

aligned & f(x)=e^ - 1 x & f^ (x)=e^ - 1 x (-1) ( -1 x^2 )= 1 x^2 e^ 1 x aligned When f ^ ( x )>0, x ^2 e ^ 1 x >0 and x 0 Now x ^2>0 and e ^ 1 x >0 for x R Hence f(x) is an increasing function for x , except x=0

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