A farmer has of fencing available to enclose three sides of a rectangular field
MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A farmer has 240m of fencing available to enclose three sides of a rectangular field, the fourth side of which lies along a straight river and requires no fencing.
(i) Let the width of the field (perpendicular to the river) be xm. Express the area A(x) of the field in terms of x.
(ii) State the admissible domain of A(x) and give a brief reason for your choice.
(iii) Find the critical point of A(x) within the domain.
(iv) Verify, using the Second Derivative Test, that the critical point obtained in part (iii) gives the maximum possible area.
(v) Determine the optimal dimensions of the field and the corresponding maximum area.