Calculus

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Find the values of a , b , and c in the quadratic function p(x)=ax2+bx+c such that p(2)=6, p'(2)=2, p"(2)=3

  • Calculus -

    p(2) = 4a + 2b + c = 6
    p'(x) = 2ax + b
    p'(2) = 4a + b = 2 ---> b = 2 - 4a
    b = 1 - 2a

    p''(x) = 2a = 3
    a = 3/2
    b = 2 - 4(3/2) = -4

    in 1st equation:
    4(3/2) - 8 + c = 6
    c = 8

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