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24 April, 08:24

Find a second-degree polynomial p such that p (1) = 5, p' (1) = 7, and p'' (1) = 10.

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  1. 24 April, 08:49
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    When p (x) = ax^2 + bx + c

    p' (x) = 2ax + b

    p'' (x) = 2a

    You require

    ... 2a = 10

    ... 2a + b = 7

    ... a + b + c = 5

    Thus a=5, b=-3, c=3, and

    ... p (x) = 5x^2 - 3x + 3
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