Maxima And Minima

Step 1: Find the derivative of :

Step 2: Find critical points by setting :

Step 3: Test the given options in :

Option (A) : Not equal

Option (B) : This satisfies the equation!

Option (C) : Outside the interval , so invalid

Option (D) : At endpoint, not in open interval

Option (E) : Same as (D), invalid

Step 4: Verify it's an extremum by second derivative test: At : This indicates a local minimum at .

Conclusion: The correct value where attains a local extremum in is ( ).