A farmer has of wire to fence three sides of a rectangular plot beside a straight…

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A farmer has

20\,\text{m}

of wire to fence three sides of a rectangular plot beside a straight river; the side along the river needs no fencing. The two sides perpendicular to the river are taken as

x\,\text{m}

each. (i) Express the area

A

of the plot as a function of

x

and state the feasible domain of

x

. (ii) Find the value of

x

that maximises

A

. (iii) Determine the maximum possible area of the plot. (iv) Justify the nature of the extremum obtained in part (ii) by examining the behaviour of the first derivative around the critical point.

Related theory

Curve Analysis
Optimization
Maxima and minima

Browse the problem library