Finding important features of graphs

[Fred Nurk]

One question in a high school textbook says to:

'[use] a CAS calculator to find the coordinates of axes intercepts and
intercepts and local maximum and local minimum values:'

<snip questions>

Is this possible in the TI-nspire (I think the book was written for
the slightly older TI calc)? I've been identifying the intercepts by
pen and paper and the local max and min values by using the Point tool
under the Points & Lines list in Graphs and Geometry

[mathletics]

Use the POINT ON tool to place a point on the graph. For polynomial
functions, the points "jump" to the zeros as you drag the point along
the graph.

I do not use the Calculus tools enough in my geometry classes to fully
appreciate how they are used.

I believe this will work for trig functions, too.

[John Hanna]

-----Original Message-----
From: tins...@googlegroups.com [mailto:tins...@googlegroups.com] On Behalf Of Fred Nurk
Sent: Friday, July 31, 2009 7:10 PM
To: tinspire
Subject: [tinspire] Finding important features of graphs

 

 

One question in a high school textbook says to:

 

'[use] a CAS calculator to find the coordinates of axes intercepts[JEH>]huh? and intercepts[JEH>]huh? and local maximum and local minimum values:'

 

[JEH>]

This seems to be looking for CAS functionality so here goes:

Use the Solve( ) command:

F1(0) for y-intercept (there’s only one if it’s a function)

Solve(f1(x)=0,x) for x-intercepts

fMin(f1(x),x) and fMax(f1(x),x) for global extrema

or

fMin(f1(x),x,a,b) and fMax(f1(x),x,a,b) for local extrema

 

fMin and fMax can give misleading results when there’s a vertical asymptote, so the better method is to use:

Solve(d(f1(x))/dx=0,x) and then use other Calculus tools to confirm extrema. Of course this always brings up functions like y=x^(2/3) J

 

On Graphical critical points: on the TI-Nspire 1.7 OS, check G&G settings (Home, 8) and make sure ‘Enable CALC menu’ is checked. Then when you trace you can also get other critical points besides extrema and zeros.

[Fred Nurk]

John Hanna wrote:
> fMin(f1(x),x,a,b) and fMax(f1(x),x,a,b) for local extrema

In G&G I assigned f1(x) = -4x^3 - 12x^2 + 37x - 15 and the above
returned:

"Error: Invalid bounds"

[Marc Garneau]

Did you specify numbers for a and b?

[Ray O'B1]

If you enable the calc menu under g&g settings in system info, you can
then find all of these items when you use Graph Trace Once you turn on
the graph trace tool, then press the ? key for shortcuts.