GeoGebra Sketches for Calc D Notes 6
Page 6. Looking at an optimization problem on a region. Akin to the Candidates Test from Calc AB.
- Turn on parametric curves a1, b1, c1, and d1.
- Turn on surfaces e, g, h, and i.
- Turn on multivariable function k.
- Turn off multivariable function f.
- Turn off surfaces e, g, h, and i.
Page 7. Looking at finding absolute extrema on a region. Basically the Candidates Test again.
- Turn on parametric curves a1, b1, and c1.
- Turn on surfaces e, g, and h.
- Turn on multivariable function d.
- Turn off function f.
- Turn off surfaces e, g, and h.
Page 8. Looking at finding absolute extrema on a region. More 3D Candidates Test.
- Turn on cylinder b.
- Turn on parametric curve a1.
- Turn off cylinder.
- Turn on multivariable function g.
- Turn off multivariable function f.
Page 11. In this sketch we look at the gradients of the constraint and the level curves of the surface.
I turned all the gradients into unit vectors so they'd fit on the sketch.
I turned all the gradients into unit vectors so they'd fit on the sketch.
- Grab point A and move it around the constraint. Watch the point B on the surface.
Page 11. In this sketch we look at the gradients of the constraint and the level curves of the surface.
In this version you can kind of see the level curve moving with the plane and...I think it helps clarify what's happening.
In this version you can kind of see the level curve moving with the plane and...I think it helps clarify what's happening.
- Grab point on the slider and drag it around. Watch what happens and pay attention to when the gradients are parallel (same direction or opposite directions).
