Find a second degree polynomial p(x) such that p(2) = 1, p'(2) = -2, and p''(2) = 3.
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Tushar Chandra
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A second degree polynomial p(x) has to be determined such that p(2) = 1, p'(2) = -2, and p''(2) = 3
Let p(x) = ax^2 + bx + c
p(2) = a*4 + b*2 + c = 1
p'(2) = 2a*2 + b = -2
p''(2) = 2a = 3
=> a = 3/2
6 + b = -2
=> b = -8
6 - 16 + c = 1
=> c = 11
The polynomial p(x) = (3/2)*x^2 - 8x + 11
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