A rectangular field uses 300 meters of fencing along three sides because a river forms the fourth side. What is the greatest possible area?

A rectangle is enclosed with 240 meters of fencing on all four sides. What maximum area can it enclose?

A garden shares one side with a wall, so 180 meters of fencing encloses its other three rectangular sides. What is the largest possible area?

A rectangular enclosure has 100 meters of fencing for all four sides. What dimensions maximize its area?

A rectangular pen uses 200 meters of fencing on three sides because the fourth side borders an existing wall. What length parallel to the wall maximizes area?

An open-top box is made by cutting squares of side $x$ from each corner of a 20-centimeter square sheet and folding up the sides. What value of $x$ maximizes volume?

Squares of side $x$ are cut from each corner of a 30-centimeter by 20-centimeter sheet to form an open box. What exact value of $x$ maximizes volume?

An open-top box has a square base and total material area of $108{\text{ cm}}^2$. What is its maximum possible volume?

A closed rectangular box has a square base, and its length plus width plus height is 24 centimeters. What is its maximum possible volume?

A closed cylindrical can holds $250{\text{ cm}}^3$. What radius minimizes its surface area, rounded to the nearest hundredth?

An open-top cylindrical container must hold $128\pi {\text{ cm}}^3$. What exact radius minimizes the material used?

A closed box with a square base must hold $256{\text{ cm}}^3$. What base-edge length minimizes surface area, rounded to the nearest hundredth?

An open-top box with a square base must hold $500{\text{ cm}}^3$. What is the minimum material area?

What point on $y=x^2$, with $x\ge 0$, is closest to $(0,4)$?

What point on the line $y=2x+1$ is closest to $(3,0)$?

A point $P=(t,t)$ lies on $y=x$. What is the minimum distance from $P$ to $(4,-2)$?

A rectangle has perimeter 80 meters. Let $w$ be its width. Which function should be maximized to find its largest area?

A rectangular garden uses 120 meters of fencing on three sides because a wall forms the fourth. Let $w$ be a side perpendicular to the wall. Which area function should be maximized?

Squares of side $x$ are cut from the corners of a 16-centimeter by 24-centimeter sheet and folded into an open box. Which volume function should be maximized?

A closed cylinder must hold $216\pi {\text{ cm}}^3$. Let $r$ be its radius. Which surface-area function should be minimized after using the volume constraint?