Build the Biggest Garden

You have 40 meters of fence. Build a rectangle to maximize the area.

Perimeter:
Area:
x = {{ state.fenceX }} y = {{ 20 - state.fenceX }} Area = {{ step1Area }} m²
Slide to maximize Maximum Found
x = 1 x = 19

Plot the Function

Let's plot the Area function:

A({{ state.graphX.toFixed(1) }}) = {{ step2Area.toFixed(1) }}
touch_app

Drag to Peak

Drag the red dot to find the maximum area.

Peak Found!

The Magic of Zero Slope

The peak occurs where the derivative (slope of tangent) is exactly zero.

Slope = {{ step3Slope.toFixed(1) }}
Tap to find zero slope
x = {{ state.slopeX.toFixed(1) }}

The Open Box Problem

Cut squares of size from a sheet. Maximize its volume.

Sheet: 12×12
x 12 - 2x
x {{ state.cutX.toFixed(1) }}
V {{ step4Volume.toFixed(0) }}
Drag to adjust cut
drag_indicator
🏆

Optimization Master!

You've successfully used functions and derivatives to find the maximum possible values in real-world problems.