SOLUTION: I have been on this for hours, if any one can please direct me.
A polynomial f(t) of degree 3 satisfies f(−2) = 0, f(2) = 4, f'(−1) = 2, and f'(1) = −6.
(a)
Algebra.Com
Question 34922: I have been on this for hours, if any one can please direct me.
A polynomial f(t) of degree 3 satisfies f(−2) = 0, f(2) = 4, f'(−1) = 2, and f'(1) = −6.
(a) Write the general form of the polynomial and its derivative.
(b) Find four linear equations that must be satisfied by the unknown coefficients in the polynomial.
(c) Write the augmented matrix for your system of equations in (b) and row-reduce.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I have been on this for hours, if any one can please direct me.
A polynomial f(t) of degree 3 satisfies f(−2) = 0, f(2) = 4, f'(−1) = 2, and f'(1) = −6.
(a) Write the general form of the polynomial and its derivative.
(b) Find four linear equations that must be satisfied by the unknown coefficients in the polynomial.
(c) Write the augmented matrix for your system of equations in (b) and row-reduce.
THE GENERAL FORM OF POLYNOMIAL OF DEGREE 3 IS
F(T)= AT^3+BT^2+CT+D ....................EQN.A
DF/DT= 3AT^2+2BT+C...................EQN.B
WE ARE GIVEN F(-2)=0...SO SUBSTITUTING IN EQN.A
-8A+4B-2C+D=0.............................EQN.I
F(2)=4...SO SUBSTITUTING IN EQN.A
8A+4B+2C+D=4................................EQN.II
F'(-1)=2...SO SUBSTITUTING IN EQN.B
3A-2B+C=2......................................EQN.III
F'(1)=-6...SO SUBSTITUTING IN EQN.B
3A+2B+C=-6..................................EQN.IV
AUGMENTED MATRIX A IS
-8,4,-2,1,0
8,4,2,1,4
3,-2,1,0,2
3,2,1,0,-6
I HOPE YOU CAN REDUCE THIS NOW AS YOU WANTED DIRECTION ...IF IN DOUBT SEE FOLLOWING EXAMPLE TO KNOW THE METHOD.
----------------------------------------------------------------------
The problem:
2x-5y+ ___=-22
__+y+3z=10
x+___+8z=15
The underscores represents blanks or O
If this had to be an augmented matrix, how would I do that and get those variables?
1 solutions
Answer 20202 by venugopalramana(1462) About Me on 2006-04-16 22:01:33 (Show Source):
2x-5y+ ___=-22...........................I
__+y+3z=10.....................II
x+___+8z=15...........................III
2*EQN.III-EQN.I
2X+16Z-2X+5Y=30+22=52
5Y+16Z=52...........................IV
EQN.IV-5*EQN.II
5Y+16Z-5Y-15Z=52-50=2
Z=2....SUBSTITUTING IN EQN.III
X+8*2=15
X=15-16=-1
SUBSTITUTING FOR Z IN EQN.II
Y+3*2=10
Y=10-6=4
USING MATRIX METHOD...AUGMENTED MATRIX IS
2 -5 0 -22 1 0 0 ?
0 1 3 10 0 1 0 ?
1 0 8 15 0 0 1 ?
NR1=R1/2
1 -2.5 0 -11
0 1 3 10
1 0 8 15
NR3=R3-R1
1 -2.5 0 -11
0 1 3 10
0 2.5 8 26
NR3=R3-2.5*R2
1 -2.5 0 -11
0 1 3 10
0 0 0.5 1
NR3=R3/0.5
1 -2.5 0 -11
0 1 3 10
0 0 1 2
NR2=R2-3R3
1 -2.5 0 -11
0 1 0 4
0 0 1 2
NR1=R1+2.5R2
1 0 0 -1
0 1 0 4
0 0 1 2
HENCE
X=-1
Y=4
Z=2
RELATED QUESTIONS
If a linear function f satisfies the given conditions, find f(x)
f(-2)= 7 and f(4)= -2
(answered by richwmiller)
Find a polynomial function f with real coefficients that satisfies the given conditions.
(answered by CubeyThePenguin)
My book doesn’t want to talk about it, they just give you the answer and that’s hopeless. (answered by venugopalramana)
Our class got assigned a project on polynomials involving writing a research paper and... (answered by MathLover1)
If f is a polynomial of degree 4 such that
f(0) = f(1) = f(2) = f(3) = 1
and
f(4) = 0,
(answered by math_helper)
my homework question is
Write a polynomial f(x) that satisfies the given... (answered by solver91311)
Hi, I am having problems understanding a problem based on the rule of a function. The... (answered by ikleyn)
Hi,
Can someone please review the following, I did the work I just want to make sure... (answered by Earlsdon)
I have been working on this for 2 days, I just do not get it. Any help would be greatly... (answered by longjonsilver)