CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
If y = 4x^3 − 6x^2 + 5x − 9, what is the value of dy/dx at x = 2?
The derivative of 4x^3 − 6x^2 + 5x − 9 is 12x^2 − 12x + 5. Substituting x = 2 gives 48 − 24 + 5, which equals 29. Each term is differentiated using the power rule and the constant disappears.
- A29Correct
- B41
- C17
- D35
Explanation
dy/dx = 12x^2 − 12x + 5. At x = 2: 12(4) − 12(2) + 5 = 48 − 24 + 5 = 29. The value 41 comes from forgetting to reduce the power of the second term (using 12x·... incorrectly) and is wrong.
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