Mathematics

Problem

The cross-sectional area

A(x)

(in square metres) of a water channel at a horizontal distance

x

metres from one end is modelled by

A(x) = \frac{x^{2} + 4x + 3}{x + 1}, \quad x > -1.

Answer the questions below. a. (a) Calculate

A'(x)

. b. (b) Find

A'(2)

and explain, in words, what this value signifies about the change in cross-sectional area at

x = 2\,\text{m}