Related Rates: Change in Cube’s Heat & Volume on TI-89

Raw Transcript

Hello everybody, Tom from EveryStepCalculus.com
I’m gonna do a related rates problem again, um and relationship to a cube.
Remember related rates always have some sort of formula to differentiate on both sides and come up with their answers. And let’s get started. index8()
to go to calculus one menu press ENTER here
you sometimes they call it average rate of change
or related rates in test
you can scroll on that one right I’m going to scroll down to
related rates there’s related rates there
I give you a list of things
keep adding to it in this case we want a cube is heated in the problem that
I’m showing here. And so we’re going to choose that
because it says a cube is heated your going to go to here
and related rates here find the rate of change in the volume
of a cube due to heating and of course here’s the formula
for the volume of a cube sided cubed
s = side and
they give you what the side
is. You have to press Alpha before we enter anything in my entry lines here.
And they give it is 12. Now they might
give you inches, feet, meters or centimeters. In this case they give you centimeters.
So I give you that choice. And then they give you the,
what’s changing with regard to heat. You have to press
Alpha. In this case they get .1. And of course they have seconds, minutes or
hours depending upon what the problem gives you. In this case they give you minutes, I’m going to Press 2.
I always show you what you’ve entered, so you can change it if you want.
Here’s 12 centimeters and .1 centimeters per minute.
I ask if it’s OK.
Here’s the answer 43.2 centimeters cubed per minute.
And, notice that your differentiating the v, volume.
And differentiating the formula
which is side cubed.
And that becomes dv/dt differentiating V.
And then we’re, we add our
derivative.
S cubed is equal to 3 S squared.
dS/dt we’re taking the derivative of
side with respect to time. And here’s three times 12
squared. And then we add the change of
rates. These are pretty easy but why not, even if they are easy, why not do it
with the program. Just so you do it within 10 seconds and be done with the problem
on a test. Then go onto something else. You can memorize it
and do it if you want. This is much better
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