TI-74: Extrema of a
Cubic Polynomial
Introduction
The
program finds the extrema points of a cubic polynomial where the roots A, B,
and C are known. The cubic polynomial is
defined as:
y
= (x – A) * (x – B) * (x – C)
Expanded to:
y
= x^3 – (A + B + C)*x^2 + (A*B + B*C + A*C)*x – (A*B*C)
The
extrema can be found by taking the derivative and then solving for x when
dy/dx=0.
dy/dx
= 3*x^2 – 2*(A + B + C)*x + (A*B + B*C + A*C) = 0
Solving
for x:
x
= (2*W ± √(4*W^2 – 12*V))/6
Where:
W
= A + B + C
V
= A*B + A*C + B*C
TI-74
Program: Extrema of Cubic Polynomials
100
PRINT “y=(x-a)(x-b)(x-c)”: PAUSE 1
110
INPUT “a: “;A
112
INPUT “b: “;B
114
INPUT “c: “;C
120
W=A+B+C
122
V=A*B+A*C+B*C
130
X1=(2*W+SQR(4*W^2-12*V))/6
132
X2=(2*W-SQR(4*W^2-12*V))/6
140
Y1=(X1-A)*(X1-B)*(X1-C)
142
Y2=(X2-A)*(X2-B)*(X2-C)
150
IMAGE “######.######, ######.######”
152
PRINT USING 150,X1,Y1: PAUSE
154
PRINT USING 150,X2,Y2: PAUSE
160
END
Example
A
= 0, B = 3, C = 5
Results:
4.119633,
-4.06067
1.213700,
8.20882
Eddie
This
blog is property of Edward Shore, 2018