2. 2025 (65/2/1)

Case Study Challenge

AOD: Street Light Intensity Patterns

A small town is analyzing the pattern of a new street light installation.

The lights are set up in such a way that the intensity of light at any point x metres from the start of the street can be modelled by the function:

f(x) = ex sin x

Where x is in metres.

Answer the following:

(i) Find the intervals on which the f(x) is increasing or decreasing for x ∈ [0, π]. [2 Marks]
(ii) Verify whether each critical point when x ∈ [0, π] is a point of local maximum or local minimum or a point of inflexion. [2 Marks]