JAMB 2021 Mathematics · Question 29
Find the derivative of the function y = 2x(2x - 1) at the point x = -1?
Options
- A.18
- B.16
- C.-4
- D.-6
Answer: B. 16
Explanation written with AI and checked against the answer key
Analyze the question: We need dy/dx of y = 2x²(2x − 1), then evaluate it at x = −1. Concept: Expand first, then differentiate using the power rule: d/dx(xⁿ) = nxⁿ⁻¹. (The product rule gives the same result.) Solution: Expand: y = 2x²(2x − 1) = 4x³ − 2x² Differentiate: dy/dx = 12x² − 4x Evaluate at x = −1: dy/dx = 12(−1)² − 4(−1) = 12 + 4 = 16 Check with the product rule: Let u = 2x², v = 2x − 1, so u' = 4x and v' = 2. dy/dx = u'v + uv' = 4x(2x − 1) + 2x²(2) = 8x² − 4x + 4x² = 12x² − 4x ✓. At x = −1: 12 + 4 = 16 ✓. Answer: 16, which is option B. Tip: When a function is a product of simple polynomials, expanding first is often faster and less error-prone than the product rule. Be careful with signs when substituting a negative value: −4(−1) = +4, which is where students often slip.AI can make mistakes. Report anything that looks wrong.
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