Question Detail
Question
Find \( a, b \) if \( (2, 2) \) is on \( y = ax^3 + bx^2 - 10 \) and gradient there is 4.
Correct Answer
Option A is the correct answer.
Detailed Explanation
( 2 = 8a + 4b - 10 \implies 2a+b=3 ). ( y' = 3ax^2 + 2bx ). ( 4 = 12a + 4b \implies 3a+b=1 ). Solving system gives ( a=-2, b=7 ).
Hint
Set up a system of two equations based on the point and the slope.