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JEE Main2012MathematicsApplication of DerivativesActual

Let f:(- , ) (- , ) be defined by f(x)=x^3+1 Statement 1: The function fhas a local extremum at x=0 Statement 2: The function f is continuous and differentiable on (- , ) and f^ (0)=0

Options

  1. AStatement 1 is true, Statement 2 is false.
  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 the correct explanation for Statement 1.
  4. DStatement 1 is false, Statement 2 is true.

Correct answer

D. Statement 1 is false, Statement 2 is true.

Step-by-step solution

Let f:(- , ) (- , ) be defined by f(x)=x^3+1 . Clearly, f(x) is symmetric along y=1 and it has neither maxima nor minima. Statement - 1 is false.

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