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Thread: Need help checking answer!!

  1. #1
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    Need help checking answer!!

    Left f(x) be a continuous function f(2)=10, f(2)=-4 and f(x)=-6 for all X. Find the value of f(2.5)
    since the slope is the derivative (-4), I plugged that in to y=mx+b and got 10=-4(2)+b, to solve for b and got 18=b. So my equation is y=-4x+18. I then solved for y, which is 8. So f(2.5)=8.....is that right?
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  2. #2
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    Re: Need help checking answer!!

    first off $f^{\prime \prime}(x) = -6,~\forall x$

    thus

    $f^\prime(x) = -6x+c_1$

    $f(x) = -3x^2 + c_1 x + c_0$

    $f^\prime(2) = -4 \Rightarrow c_1 = 8$

    so $f(x) = -3x^2 + 8x + c_0$

    $f(2) = 10 \Rightarrow c_0 = 6$

    $f(x) = -3x^2 + 8x + 6$

    $f(2.5) = 7.25$
    Thanks from topsquark
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  3. #3
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    Re: Need help checking answer!!

    Quote Originally Posted by tomas View Post
    Left f(x) be a continuous function f(2)=10, f’(2)=-4 and f’’(x)=-6 for all X. Find the value of f(2.5)
    since the slope is the derivative (-4), I plugged that in to y=mx+b and got 10=-4(2)+b, to solve for b and got 18=b. So my equation is y=-4x+18. I then solved for y, which is 8. So f(2.5)=8.....is that right?
    You are assuming that the function is linear which can't be true because a linear function has second derivative 0, not -6.
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