November 2025 (9709/12). Question 9 (Also covers “Functions” topic)

The function f is defined by

(a) Find an expression for f'(x) and hence determine whether f is an increasing function, a decreasing function or neither. [4 marks]

(b) State whether f^-1 exists. Give a reason for your answer. [1 mark]

The function g is defined by g(x) = 4x – 3 for x > a.

(c) Find the set of values of a for which the composite function fg exists [2 marks]

9709/11/M/J/25q7

The equation of a curve is .

(a) A point P is moving along the curve in such a way that its y-coordinate is decreasing at 5 units per second.

Find the rate at which the x-coordinate of point P is changing when x = 2. [4 marks]

(b) Find the coordinates of the stationary points of the curve and determine their nature. [5 marks]

9709/12/M/J/25q4

A point P is moving along the curve with equation in such a way that the x-coordinate of P is increasing at a constant rate of 5 units per second.

(a) Find the rate at which the y-coordinate of P is changing when x = 9. Give your answer in terms of the constant a. [3 marks]

(b) Given that the curve has a minimum point when , find the value of a. [2 marks]