If the function , where attains its maximum and minimum at and respectively such that , then equals
Explanation for the correct option
Step 1: Solve for the extremities of the given function
Given that the function where attains its maximum and minimum at and respectively such that
For maxima and minima of the function
Differentiating with respect to we get
Differentiating with respect to we get
Equating to we get,
and
Thus, the function has a maxima and a minima at either of or
Step 2: Solve for the required value
When at a point , the function has a maxima at that point
Hence, has a maxima at
When at a point , the function has a minima at that point
Hence, has a minima at
We know that,
or
As ,
Thus, the required value of is .
Hence, option (C) i.e. is the correct answer.