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Thread: 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?
    $\displaystyle f(2) = 10$ ...

    $\displaystyle 10 = a(2)^3 + b(2)^2 + 3(2) - 2$

    do the same for $\displaystyle f'(-1) = 14$ ... then solve the system of equations for $\displaystyle a$ and $\displaystyle b$
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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.


    $\displaystyle 10 = a(2)^3 + b(2)^2 + 3(2) - 2$

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

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

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

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

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

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

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