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JEE Main2013MathematicsApplication of DerivativesActual

Statement-1: The equation x x=2-x is satisfied by at least one value of x lying between 1 and 2. Statement-2: The function f(x)=x x is an increasing function in [1,2] and g(x)=2-x is a decreasing function in [1,2] and the graphs represented by these functions intersect at a point in [1,2]

Options

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

Correct answer

A. Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Step-by-step solution

f(x)=x x, f(1)=0, f(2)=4g(x)=2-x, g(1)=1, g(2)=0 10> 4 1> 4 Thus statement -1 and 2 both are true and statement-2 is a correct explanation of statement 1 .

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