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 the change in y when x changes by Δx, so Δy = f(x + Δx) - f(x).Given f(x) = 3x².f(x + Δx) = 3(x + Δx)² = 3(x² + 2xΔx + (Δx)²) = 3x² + 6xΔx + 3(Δx)².Δy = (3x² + 6xΔx + 3(Δx)²) - 3x²Δy = 6xΔx + 3(Δx)².
Hint
The increment Δy is defined as f(x + Δx) - f(x). Expand f(x + Δx) carefully.