Graphing the derivative


When you have a function f(x) stored in \Y1, and you want to graph its first (and second) derivatives, just put


\Y2=nDeriv(Y1,X,X)          first derivative f'(x) of f(x)

\Y3=nDeriv(Y2,X,X)          second derivative f"(x) of f(x)



On this calculator you cannot compute the third derivative in this way. You'll get a message, ILLEGAL NEST.


The only problem is how to set the window.

Here is one way:


Assuming that you want to graph the second derivative between the values a and b. (##)

Set Xmin=a, and Xmax=b.

From the home screen, compute

Y3(a+(b-a)rand(10))→L1          ENTER

(See the explanation for this at ** below.)

Now under WINDOW, set Ymin=min(L1), and Ymax=max(L1). Graph Y3, and adjust the window.


Example 1.



\Y3=nDeriv(Y2,X,X)          only Y3 is selected


a=4, b=9, (mode: radians)


Y3(4+5rand(10)) →L1

{6.495122105 4.9...







Ymax=max(L1)          this is what you enter




(WINDOW required only a small adjustment.)



Explanation of the code Y3(a+(b-a)rand(10))→L1

rand(10) creates a sequence of 10 numbers between 0 and 1;

(b-a)rand(10) transforms it into a sequence of numbers between 0 and (b-a);

so, a + (b-a)rand(10) creates a sequence of numbers between a +0 = a and a + (b – a) = b, which is the domain on which we want to graph the second derivative (marked ## above).


Example 2, from the unit Making an open box with maximal volume. Lets graph the first derivative.


\Y2=nDeriv(Y1,X,X)          first derivative f'(x) of f(x)

We know the domain of X: from 0 to 4.5.

We need to find a reasonable range of Y.


From the home screen, enter

Y2(0+ (4.5-0)rand(10)) →L1

You will get 10 random numbers stored in L1.

In WINDOW, set Ymin=min(L1)


I prefer to put AXES ON.

Now GRAPH. (You may have both Y1 and Y2 highlighted.)



You may want to change Ymin to be smaller:

Webpage implementation by Aous Manshad l last modified : September 11, 2011