Let f(x)=x2−92x2−3x+1. Answer the following questions.
(i) State the domain of f(x).
(ii) Explain, without performing any calculations, why f′(x) is not defined at x=±3.
(iii) Describe how the sign of the denominator near x=3 influences the sign of f′(x) in a left–hand neighbourhood and a right–hand neighbourhood of x=3. Give a brief justification based on the algebraic form of the derivative.