Maths-
General
Easy

Question

A function f is defined by f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x inleft square bracket 0 comma blank pi right square bracket. Which of the following is not correct?

  1. f is continous in open square brackets 0 comma blank pi close square brackets  
  2. f is differentiable in left square bracket 0 comma blank pi right square bracket  
  3. f open parentheses 0 close parentheses equals f left parenthesis pi right parenthesis  
  4. Rolle’s theorem is not true in left square bracket 0 comma blank pi right square bracket  

The correct answer is: Rolle’s theorem is not true in left square bracket 0 comma blank pi right square bracket


    Given, f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x comma blank x element of open square brackets 0 comma blank pi close square brackets
    At x equals 0 comma blank f open parentheses 0 close parentheses equals 0

    And at x equals pi comma blank f open parentheses pi close parentheses equals 0

    Also, it is continuous and differentiable in the given interval.

    Hence, it satisfies the Rolle’s theorem.

    Hence, option (d) is the required answer

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