CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
If y = (x^2 + 3)/(x + 1), what is dy/dx at x = 1?
Using the quotient rule, dy/dx = [2x(x + 1) − (x^2 + 3)]/(x + 1)^2. At x = 1 the numerator is 2×2 − 4 = 0, so the derivative is 0.
- A1/2
- B0Correct
- C1
- D2
Explanation
Quotient rule: dy/dx = [2x(x + 1) − (x^2 + 3)(1)]/(x + 1)^2. At x = 1: [2(2) − 4]/4 = 0. Option 1/2 arises from subtracting in the wrong order only partly; the numerator is 4 − 4 = 0.
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