ID: Class: 12 Subject: Math Topic: Application of Derivative Type: Case Study Year: 2025

Question:

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 \(f(x)=e^{x} \sin x,\) where \(x\) is in metres.

Based on the above, answer the folowing

(i) Find the intervals on which the \(f(x)\) is increasing or decreasing, \(x\in[0,\pi]\). (2 marks)

(ii) Verify, whether each critical point when \(x\in[0,\pi]\) is a point of local maximum or local minimum or a point of inflexion. (2 marks)