Question Detail
Question
Stationary point of \( y = x(x^2 - 128\sqrt{x}) \) is at?
Correct Answer
Option A is the correct answer.
Detailed Explanation
( y = x^3 - 128x^{3/2} \implies y' = 3x^2 - 192x^{1/2} = 0 \implies x^{3/2} = 64 \implies x = 16 ). At 16, ( y = 16(256 - 128(4)) = -4096 = -2^{12} ).
Hint
Simplify the expression and find where the derivative equals zero.