Question Detail
Question
Find the coordinate of \( Q \) for \( y = 2x^3 - 9x^2 + 12x - 10 \) where gradient is same as at \( x = -1 \).
Correct Answer
Option A is the correct answer.
Detailed Explanation
( y' = 6x^2 - 18x + 12 ). At ( x = -1, y' = 6+18+12 = 36 ). Set ( 6x^2 - 18x + 12 = 36 \implies x^2 - 3x - 4 = 0 \implies (x-4)(x+1) = 0 ). Point ( Q ) is at ( x=4 ), ( y = 2(64) - 9(16) + 12(4) - 10 = 22 ).
Hint
Solve the quadratic equation formed by the derivative.