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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