### Home > PC > Chapter 9 > Lesson 9.3.2 > Problem9-114

9-114.

A rectangular corral is to be built using $900$ ft of fencing. Three sides will need fencing. The fourth side will border a river. The goal is to make a rectangular corral that has the maximum possible area under these conditions.

1. Sketch the situation.

2. Write an equation for the area of the corral as a function of $x$, the length of the side perpendicular to the river.

$2x + y = 900$
$y = 900 − 2x$
Area $= \left(x\right)\left(900 − 2x\right)$

1. Graph this function.

first quadrant Downward parabola, turning at (225, comma 101,250), x-intercepts at 0 & 450.

2. Which value of $x$ gives you the maximum area?

Coordinates at turning point added, (225, comma 101,250)

3. What is the slope of the tangent line to the area graph at this point?

Slope of the tangent line is $0$.