Mathematics

Problem

A quantity

y

varies with

x

according to

y=(x^{2}+1)(x-3)

. a. (i) Obtain

\dfrac{dy}{dx}

using an appropriate rule. b. (ii) Express the result from part (i) entirely in Lagrange notation

f'(x)

, clearly identifying

f(x)

. c. (iii) Evaluate the derivative at

x=3

in both notations. d. (iv) If

y

represents distance (in metres) and

x

represents time (in seconds), interpret the numerical answer from part (iii) in physical terms.