The cross-sectional area (in square metres) of a water channel at a horizontal…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
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)=x+1x2+4x+3,x>−1.
Answer the questions below.
(a) Calculate A′(x).
(b) Find A′(2) and explain, in words, what this value signifies about the change in cross-sectional area at x=2m.