Mathematics

Problem

A rectangular field is to be fenced on three sides only, as one side lies along a straight river and needs no fencing. If

600\,\text{m}

of fencing material is available, the two equal shorter sides are of length

x

metres while the longer side parallel to the river is of length

y

metres. a. (i) Express the area

A

of the field in terms of

x

only. State clearly the permissible range of

x

. b. (ii) Obtain

\dfrac{dA}{dx}

and find all critical points of

A

in the domain stated in part (i). c. (iii) Determine the dimensions of the field that maximise the area and calculate this maximum area. d. (iv) Give a brief explanation why the area found in part (iii) is the absolute maximum for all admissible values of

x

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