Question Detail
Question
Find the coordinates of the local maximum for \( y = x^2 - 6\sqrt{x^4} + 2 \).
Correct Answer
Option A is the correct answer.
Detailed Explanation
( y' = 2x - 8x^{1/3} ). For stationary points, ( 2x - 8x^{1/3} = 0 \implies x=0, 8 ). At ( x=0 ), ( y=2 ). Gradient check to the right shows a decrease, identifying it as a max.
Hint
Find the first derivative and check the sign of the gradient around critical points.