Correct Answer - Option 2 : Minimum
Concept:
A function attains a minimum value at a given point if the double derivative of that function at that point is positive.
A function attains a maximum value at a given point if the double derivative of that function at that point is negative.
Calculations:
Given function is \(y = x^2 + \dfrac{250}{x}\)
Differentiating both sides w.r.t. x , we get ,
\(dy \over dx \) = 2x - \(250 \over x^2\)
Putting \(dy \over dx \) = 0 , we get ,
2x - \(250 \over x^2\) = 0
Solving the above equation, we get,
x = 5
Now, \(d^2y \over d^2x\) = 2 + \(500 \over x^3\)
Putting x = 5 in the above equation, we get ,
\(d^2y \over d^2x\) = 6, which is positive.
So, the function attains a minimum value at x = 5
