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Math Help - higher-order derivatives

  1. #1
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    higher-order derivatives

    find a quadratic function f such that f(3)=33, f'(3)=22, f''(3)=8
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    find a quadratic function f such that f(3)=33, f'(3)=22, f''(3)=8
    start with f(x) = ax^2 + bx + c

    since f(3) = 33 ... 33 = a(9) + b(3) + c


    f'(x) = 2ax + b

    since f'(3) = 22 ... 22 = 2a(3) + b


    f''(x) = 2a

    since f''(3) = 8 ... 8 = 2a


    so ... find a, b, and c.
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  3. #3
    Super Member malaygoel's Avatar
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    Quote Originally Posted by skeske1234 View Post
    find a quadratic function f such that f(3)=33, f'(3)=22, f''(3)=8
    Assume f(x)=ax^2+bx+c

    Now, apply the given conditions and determine a,b,c.
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  4. #4
    MHF Contributor Bruno J.'s Avatar
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    Or you can use the Taylor series of the polynomial about x=3, and not have to solve for any unknowns:

    f(x)=f(3)+\frac{f'(3)}{1!}(x-3)+\frac{f''(3)}{2!}(x-3)^2<br />
=33+22(x-3)+4(x-3)^2 = 4x^2-2x+3
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