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JEE Main2012MathematicsContinuity and DifferentiabilityActual

Consider the function f(x)=|x-2|+|x-5|, x R . Statement 1 : f^ (4)=0 Statement 2 : f is continuous in [2,5] , differentiable in (2,5) and f(2)=f(5) .

Options

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

Correct answer

B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

Step-by-step solution

f(x) =7-2 x ; x 5f(x) is constant function in [2,5]f is continuous in [2,5] and differentiable in (2,5) and f(2)=f(5) by Rolle's theorem f^ (4)=0 Statement 2 and statement 1 both are true and statement 2 is correct explanation for statement 1 .

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