Plot derivative of a function

[CR Haeger]

(06-04-2014 06:56 AM)Wes Loewer Wrote:  

(06-02-2014 05:59 AM)cyrille de brébisson Wrote:  the syntaxe: dF1(X)/dX=value is a shorthand for dF1(X)/dX | X=X (|=WHERE)

The math purist might prefer dF1(T)/dT=X for dF1(T)/dT | T=X. It seems clearer written this way as it shows that you're taking a derivative with respect to a variable, T, then evaluating it at a value, X.

I strongly discourage students from writing things like the above or ∫(F1(x),x,0,x) in which the x has two different meanings. And by "strongly discourage" I mean I take off a token point on a test. :-)

-wes

Wes - thank you for your guidance and I hope I didnt stir up a bees nest suggesting that dual use of X was mathematically correct.

From my practical user (Engineer) standpoint, I was looking for ways to graphically display how the first derivative or slope of f(x) or F1(X) changed over a range of x values. In the Prime Function App, we are required to use upper case X only to represent "independent x axis" values. If T or other variables could be substituted for the independent variable then I might use it. That is also why I suggested the use of the slope() function.

This also seems to apply to the integral or area() commands where I might want to display how the area changes over a varying (0-->X?) lower/upper limits for f(x).

In CAS, I also have used solve() and fsolve() with derivatives, definate integrals using lower case x for both the independent variable and the variable to solve for. Ive also used other variables ("a" in this case). Both seem to work. Maybe this is also not mathematically correct.

   

In my limited experience with TI36 and TI84 calculators, they also allow for the dual meaning of X in first derivatives and integrals.

Best,
Carl