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JEE Main2013MathematicsApplication of DerivativesActual

Statement-1: The function x^2 (e^x+e^ -x ) is increasing for all x>0 . Statement-2: The functions x^2 e^x and x^2 e^ -x are increasing for all x>0 and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b) .

Options

  1. AStatement-1 is false; Statement-2 is true.
  2. BStatement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  3. CStatement-1 is true; Statement-2 is false.
  4. DStatement-1is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.

Correct answer

C. Statement-1 is true; Statement-2 is false.

Step-by-step solution

Let y=x^2 e^ -x For increasing function, aligned & d y d x >0 x [(2-x) e^ -x ]>0 & x>0, (2-x) e^ -x >0 & (2-x) 1 e^x >0 & For 0 < x < 2,(2-x) < 0 & 1 e^x < 0, but it is not possible aligned Hence the statement- 2 is false.

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