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Math Help - Determine the values of a and b for the function.

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    Determine the values of a and b for the function.

    Determine the values of a and b for the function f(x)=ax^3 +bx^2 +3x -2 given that f(2)=10 and f'(-1)=14.

    Where would I start?
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  2. #2
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    Quote Originally Posted by kmjt View Post
    Determine the values of a and b for the function f(x)=ax^3 +bx^2 +3x -2 given that f(2)=10 and f'(-1)=14.

    Where would I start?
    f(2) = 10 ...

    10 = a(2)^3 + b(2)^2 + 3(2) -  2

    do the same for f'(-1) = 14 ... then solve the system of equations for a and b
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    f(x)=ax^3 +bx^2 +3x -2

    f'(x) = 3ax^2 +2bx +3 -2

    14 = 3a(-1)^2 +2b(-1) +3

    If thats what you mean. What would I do now? I'm not really sure how to isolate a or b.
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    Quote Originally Posted by kmjt View Post
    f(x)=ax^3 +bx^2 +3x -2

    f'(x) = 3ax^2 +2bx +3 -2

    14 = 3a(-1)^2 +2b(-1) +3

    If thats what you mean. What would I do now? I'm not really sure how to isolate a or b.
    You have two equations and two variables. Solve them simultaneously.


    10 = a(2)^3 + b(2)^2 + 3(2) -  2

    \Rightarrow 8a+4b-6=0 \rightarrow\color{red}{(1)}

    --------------------------------------------------------

    14 = 3a(-1)^2 +2b(-1) +3

    \Rightarrow 3a -2b - 11=0 \Rightarrow a= \frac{2b+11}{3} \rightarrow\color{red}{(2)}

    --------------------------------------------------------

    Now sub \color{red}{(2)} into \color{red}{(1)}.

    \Rightarrow 8(\frac{2b+11}{3})+4b-6=0
    Last edited by Anonymous1; April 2nd 2010 at 06:26 PM. Reason: clarity is next to godliness.. Wait?
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    Got it thanks
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