Thursday, December 17, 2009

Optimization with Calculus 2

Technology does have its advantages. One of my AP kids just sent me this video with a note saying how helpful it was as well as entertaining.

Who would have guessed that You tube could be so educational.


jonathan said...

So we get volume in terms of x:

V(x) = x(24-2x)^2

wait... stop... Product rule's available. No need to multiply out:

V'(x) = x(2)(24-2x)(-2) + 1(24-2x)^2

factor out a 24 - 2x

V'(x) = (24-2x)[-4x + (24 - 2x)]
V'(x) = (24-2x)(24-6x)

prefactored and everything. Pretty cool, I think.


Pissed Off said...

The kids find this problme easier when they multiply out first. But, I would do the problme myself the way you described.

mathematicamama said...

What class is this being taught in? My daughter did this 2 months ago in AlgTrig.

Pissed Off said...

We teach optimization in pre-calc but it goes to a whole new level when you introduce derivatives. Your daughter must be in a very advanced class if she is studying rates of change with calculus.

Anonymous said...

In Alg2, writing the volume as a function of the side of the little square might be a nice problem.

For quadratic functions (which this is not) they have been teaching kids in Alg2 (and even Alg1) to use the symmetry of the curve to find max or min.

But this problem - can't see how to do it without derivatives (or messy and inconclusive trial and error).

By the way, I would have (or should have) restricted the domain before starting the manipulation. Bad on me. x goes from 0 to 12, not including 0 or 12.


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