This program calculates the coefficients of the derivative and the integral of a polynomial. The maximum degree of the polynomial can be is seven.

The variables of the polynomial are:

H x^7 + G x^6 + F x^5 + E x^4 + D x^3 + C x^2 + B x + A

Instructions:

1. ** Load the Polynomial. ** Press XEQ P001, enter the degree of the polynomial and load the coefficients from the highest degree to the constant.

2. ** Operation. ** To find the derivative, press XEQ P033. For an indefinite integral, press XEQ P083.

**Program **

' Start of program

' Messages in quotes can be typed by pressing the EQN key. Each letter is typed as so: RCL * letter *.

' To set/clear flag 10 press Gold Shift FLAGS. 1 for Set, 2 for Clear. "Type" 10 by pressing the decimal point followed by the zero.

P001 LBL P

P002 SF 10

P003 "DEGREE"

P004 PSE

P005 CF 10

P006 INPUT N

P007 1

P008 +

P009 STO M

P010 SF 10

P011 "X^"

P012 PSE

P013 RCL M

P014 1

P015 -

P016 PSE

P017 1

P018 +

P019 +/-

P020 STO I

P021 "COEF"

P022 PSE

P023 CF 10

P024 RCL(I)

P025 STOP

' STOP is entered by pressing R/S

P026 STO(I)

P027 DSE M

P028 GTO P010

P029 SF 10

P030 "DONE"

P031 CF 10

P032 RTN

' Derivative Routine

P033 1

P034 RCL+ N

P035 STO M

' Calculate the coefficients

P036 RCL M

P037 +/-

P038 STO I

P039 +/-

P040 -1

P041 RCL+ M

P042 STOx(I)

P043 DSE M

P044 GTO P036

' Shift the coefficients to the appropriate slots

P045 2

P046 1

P047 RCL+ N

P048 1000

P049 ÷

P050 +

P051 STO M

P052 RCL M

P053 IP

P054 +/-

P055 STO I

P056 RCL(I)

P057 1

P058 STO+ I

P059 R↓

P060 STO(I)

P061 ISG M

P062 GTO P052

P063 RCL N

P064 +/-

P065 1

P066 -

P067 STO I

P068 0

P069 STO(I)

' Display Routine

P070 RCL N

P071 STO M

P072 RCL M

P073 +/-

P074 STO I

P075 VIEW(I)

P076 DSE M

P077 GTO P072

P078 SF 10

P079 "DONE"

P080 PSE

P081 CF 10

P082 RTN

' Integral Routine

' Calculate the coefficients

P083 1

P084 RCL +N

P085 STO M

P086 RCL M

P087 +/-

P088 STO I

P089 +/-

P090 1/x

P091 STOx(I)

P092 DSE M

P093 GTO P086

' Shift the coefficients into the proper place

' The constant term is assigned 0 (technically, it is an arbitrary constant)

P094 1

P095 RCL+ N

P096 STO M

P097 RCL M

P098 +/-

P099 STO I

P100 1

P101 -

P102 RCL(I)

P103 x<>y

P104 STO I

P105 x<>y

P106 STO(I)

P107 DSE M

P108 GTO P097

P109 0

P110 STO A

' Display Routine

P111 RCL N

P112 2

P113 +

P114 STO M

P115 RCL M

P116 +/-

P117 STO I

P118 VIEW(I)

P119 DSE M

P120 GTO P115

P121 SF 10

P122 "DONE"

P123 PSE

P124 CF 10

P125 RTN

' End of Program

Memory: LN=433

**Example**

Find the derivative and integral of f(x) = x^3 - 2x^2 + 1

Derivative:

1. XEQ P001

2. Enter 3 at DEGREE prompt, then press R/S

3. "X^3" : 1, R/S

4. "X^2" : -2, R/S

5. "X^1" : 0, R/S

6. "X^0" : 1, R/S

7. XEQ P033. Press R/S after each coefficient.

Then f'(x) = 3x^2 - 4x

For the integral:

1. XEQ P001

2. Enter 3 at DEGREE prompt, then press R/S

3. "X^3" : 1, R/S

4. "X^2" : -2, R/S

5. "X^1" : 0, R/S

6. "X^0" : 1, R/S

7. Press XEQ P083.

Then the integral is .25x^4 - .6666666667x^3 + x

Recall that the variables of the polynomial are:

H x^7 + G x^6 + F x^5 + E x^4 + D x^3 + C x^2 + B x + A