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)

 

Remark

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.

\Y1=Xsin(X)+.5X^2

\Y2=nDeriv(Y1,X,X)

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

 

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

 

Y3(4+5rand(10)) →L1

{6.495122105 4.9...

 

WINDOW

Xmin=4

Xmax=9

...

Ymin=min(L1)

Ymax=max(L1)                      this is what you enter

...

 

GRAPH

(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.

\Y1=(11-2X)(8.5-2X)X

\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)

Ymax=max(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