Observation 5 - Honing in Partials
Last time:
- Find
for . - Simplify
- Evaluate at
- Draw Level Curves for various levels
Let's see how they did:
- They looked at
and got the level of . - They determined that
is the level curve through . Good job!!! - They forgot a bit about how to determine a restricted domain
They looked at the 3D image of this, and now want to find the partial derivatives: . They surprisingly got the derivative of quickly. - He really wants them to simplify:
.
- He really wants them to simplify:
. Again they need to simplify . - They evaluate at
- They needed to parameterize the lines made intersecting
and the planes - They actually seemed to get the parameterization idea pretty nailed down already!
What was good is that Brussel asked them what the partial derivative means? They got that it was the slope of the function over the parameterized lines!!!
- They can make
and find from the parametrized curve - They can do the rise/run thing using
ad the rise and the magnitude of as the run. - They did the same thing with
Someone asked about what we mean by parametrized curve, so it may be good to review this in more detail