CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
If y = (2x + 1)(x² − 3), what is dy/dx at x = 2?
Using the product rule, dy/dx = 2(x² − 3) + (2x + 1)(2x). At x = 2 this equals 2 + 20 = 22, confirmed by expanding the product first.
- A26Correct
- B30
- C34
- D22
Explanation
Product rule: dy/dx = 2(x² − 3) + (2x + 1)(2x). At x = 2: 2(1) + 5(4) = 2 + 20 = 22. Expanding first gives y = 2x³ + x² − 6x − 3, so dy/dx = 6x² + 2x − 6 = 24 + 4 − 6 = 22. The correct value is 22.
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