ok, so I have a question about to do this on the TI-89.

determine intervals where function f(x)=(x^2)/(x^2+1) is increasing and intervals where it is decreasing.

6/24/2008 11:31:50 PM

plot the derivate; it's increasing where the derivate is positive, decreasing where it's negative

6/24/2008 11:36:37 PM

i pray you don't need a calculator to do this.

6/24/2008 11:56:36 PM

you shouldnt be learning how to do stuff on the calculator. Besides maybe graphing, calculators should be used for nothing more than helping to speed up basic math (and play games ) People dont know how to do this math anymore, only how to plug it into calculators. And then they dont know how or why stuff is done.

i know its a pain, but it is really beneficial to do as much by hand as you can.

[Edited on June 25, 2008 at 9:06 AM. Reason : ]

6/25/2008 9:05:10 AM

yeah well, last math class, won't be using this in the real world, just looking to learn the calc and pass.

6/25/2008 10:23:48 AM

This is how you do it by hand.

Find the derivative of the function using the Quotient Rule.

Then find all critical numbers. This will include all values of x which will make the derivative undefined(set denominator = 0 and solve) and all values of x which makes the derivative = 0(numerator = 0 and solve).

Then plot all of these numbers on a number line.
Choose a number on each interval that is created on this number line and plug it into the derivative. If the answer is positive, then the function is increasing. If the answer is negative, then the function is decreasing.

I know you probably don't care why it works but this is how it works. One of the uses of a derivative is to tell you the slope of a line that is tangent to the curve at any given point. If the function is increasing then the slope is positive. If the function is decreasing then the slope is negative. If the slope = 0, then the point is a min/max and you can tell this by looking at the different signs on the number line technique i described earlier.

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But if you must do it using a calculator, this is how...

1) Find all relative maxs/mins by looking at the graph and using max/min capabilities of the 89.
2) Then determine if the slope of the graph is positive or negative before and after each max/min.

then your answer is sitting in front of you...

Ex. If your maxs/mins are at -1, 3, 5, then you will need to look at the graph before -1, between -1 and 3, between 3 and 5, and after 5

[Edited on June 25, 2008 at 11:08 AM. Reason : calc]

6/25/2008 11:02:31 AM

gracis StayPuff.

exactly what I was looking for, instead of an admonishment of me using available technology to do the work.

6/25/2008 11:05:32 AM

This turns out to be a really nice and easy problem.

Only 1 critical number so you would only have 2 intervals. One will be positive and the other is negative

6/25/2008 11:15:43 AM

sorry didnt have time to go in depth, im doing calcs of my own atm heh

[Edited on June 25, 2008 at 11:25 AM. Reason : ]

6/25/2008 11:24:33 AM

Sadly it seems like education is expecting more use of technology to solve problem instead of doing it by hand...even if it is simple.

Look at our schools. We have students that can't do basic operations with numbers without a calculator. In fact, it is very hard to pass the Alg 1 EOC without the calculator now.

Thankfully I am teaching Calculus, Stats, and Probability next year...at least most of my students will know the basics.

6/25/2008 11:38:35 AM

not to sound like an ass, but I just don't care if I can do it without a calculator. the class I took was just to add another math credit so I can graduate, I've already finished all the other shit I have to do, and the class that I "needed" wasn't offered during the summer, so I had to take this one. So otherwise, I would have never (normally) taken this class anyway, with no real need of knowing 90% of the shit I learned in said class.

job is already obtained, just wrappin up the last 3 classes of "elective" type shit.

6/25/2008 3:35:03 PM