Question $1$: A cylindrical tank $is$ being filled with water $at$ a rate $of5\frac{m^3}{m}$inV $h\frac{m}{m}in$ and the radius $of$ the tank $is3$ meters.

Question $2$: A rectangular garden with length I and width $wistobe$ fenced along three sides, with the fourth side along the

bank $of$ a river, $as$ illustrated $in$ the diagram. You have $150$ meters $of$ fencing available, and $no$ fencing $is$ needed along the

riverbank.

$a.$ Express the area $of$ the garden $as$ a function $of$ its width $w,$ given the constraint $on$ the total length $of$ the fencing.

$b.$ Determine the dimensions $of$ the garden that will maximize the enclosed area.

$c.$ Verify the dimensions found $in$ part $2(b)by$ checking the second derivative $to$ confirm whether they provide $a$

maximum area.

$d.$ Calculate the maximum possible area enclosed with the available fencing using the dimensions found $in$ part $2(b).$