CAIE A-Level Mathematics AS 2.4.2 Product and Quotient Rules Questions

Practise statistical regression methods within the AS mathematics syllabus.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 3]

Figure for Question CAIE A-Level Mathematics AS 2.4.2 Product and Quotient Rules Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve with equation $y=\frac{2 \ln x}{3 x+1}$ . The curve crosses the x-axis at the point A and has a maximum point B. The shaded region is bounded by the curve and the lines x=3 and y=0.

Find the gradient of the curve at A.

Differentiate using quotient rule (or product rule)
Obtain $\frac{(3 x+1) \frac{2}{x}-6 \ln x}{(3 x+1)^{2}}$
OE

Substitute x=1 to obtain $\frac{1}{2}$
OE

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CAIE A-Level Mathematics AS 2.4.2 Product and Quotient Rules Questions question 1