- #1
Mathman23
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Hi
I have obtain two third degree polynomials p and q which are determint by the following conditions:
p(-1) = 1 , p'(-1) = 0
q(1) = 3 , q'(1) = 0
p(0) = q(0) , p'(0) = q'(0)
where p = a_1 * x^3 + b_1 *x^2 + c_1 *x + d_1
q = a_2 * x^3 + b_2 *x^2 + c_2 *x + d_2
I then end up with the the following linear equations by inserting the conditions into the equations above:
-a_1 + b_1 - c_1 + d_1 = 1
3* a_1 - 2 * b-1 + c_1 = 0
c_1 = d_1
3* a_2 + b_2 + c_2 + d_2 = 3
3 * a_2 + b_2 + c_2
d_1 = d_2
By the use of substitution I obtain the result, that
a_1 = 1/5 , b_1 = 34/5 , c_1 = d_1 = -15/5
My question is it correct to use substitution? If yes can I use approach to obtain a_2, b_2, c_2 and d_2 ?
Sincerley
Fred
I have obtain two third degree polynomials p and q which are determint by the following conditions:
p(-1) = 1 , p'(-1) = 0
q(1) = 3 , q'(1) = 0
p(0) = q(0) , p'(0) = q'(0)
where p = a_1 * x^3 + b_1 *x^2 + c_1 *x + d_1
q = a_2 * x^3 + b_2 *x^2 + c_2 *x + d_2
I then end up with the the following linear equations by inserting the conditions into the equations above:
-a_1 + b_1 - c_1 + d_1 = 1
3* a_1 - 2 * b-1 + c_1 = 0
c_1 = d_1
3* a_2 + b_2 + c_2 + d_2 = 3
3 * a_2 + b_2 + c_2
d_1 = d_2
By the use of substitution I obtain the result, that
a_1 = 1/5 , b_1 = 34/5 , c_1 = d_1 = -15/5
My question is it correct to use substitution? If yes can I use approach to obtain a_2, b_2, c_2 and d_2 ?
Sincerley
Fred