GeoGebra
Home
News Feed
Resources
Profile
People
Groups
App Downloads
GeoGebra
Inscribed Rectangle under a Parabola
Author:
cconrad
Topic:
Parabola
,
Rectangle
What is the area of the largest rectangle that you can inscribe between the parabola
and the x-axis?
Using Geogebra to explore this problem.
Use the left-window to enter the equation. It is important to use
notation.
Plot point A on the x-axis (if you did it right, it should be sky blue)
Use the reflect tool to reflect A over the y-axis
Use the left-window to plot the following two points. (x(A),f(x(A)) (x(A’),f(x(A’))
Switch to the Arrow Tool. If this was done correctly, all 4 points should move when you drag point A.
Use the Polygon tool to draw a polygon around the 4 points. Poly1 in the left-window shows the area of the rectangle.
Drag A until the area is at a maximum (keep the rectangle above the x-axis)
Questions
What is the maximum area?
What value of x that maximized the area?
What is the base length?
What is the height?
The area of a rectangle is
. What is the base length in terms of x? What is the height in terms of x? What is the area?
Find the derivative of the area and use this to find when the area of the rectangle has a maximum value.
Related Topics
Ellipse
Hyperbola
General Quadrilateral
Kite
Parallelogram
Discover Resources
Introduction to Solving Trig Equations #2
quadratic function
Visualisatie2
geogebra
x raised to an even power
Discover Topics
Derivative
Arithmetic
Polygons
Logarithm
Trigonometric Functions