Question Detail
Question
If y = 3x², the increment Δy is:
Correct Answer
Option A is the correct answer.
Detailed Explanation
The increment Δy is defined as f(x + Δx) - f(x).Given f(x) = 3x².Δy = 3(x + Δx)² - 3x²Δy = 3(x² + 2xΔx + (Δx)²) - 3x²Δy = 3x² + 6xΔx + 3(Δx)² - 3x²Δy = 6xΔx + 3(Δx)²This matches option A.
Hint
Recall the definition of increment Δy = f(x + Δx) - f(x). Substitute the given function and expand the expression.