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Math Help - Tangent line approximation help?

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    Tangent line approximation help?

    For this question: Tangent line approximation help?-capture7.jpgI'm having a lot of trouble figuring out f(0). Can anyone help? I know that f'(-0.5)=4 which means that f(4)=-0.5 and I know that f(-0.5)=2 which means that f'(2)=-0.5, right? But I don't know how to relate this to tangent line approximation and find f(0). Can anyone explain this to me? Thanks!
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    Re: Tangent line approximation help?

    Quote Originally Posted by canyouhelp View Post
    For this question: Click image for larger version. 

Name:	Capture7.JPG 
Views:	7 
Size:	17.8 KB 
ID:	30700I'm having a lot of trouble figuring out f(0). Can anyone help? I know that f'(-0.5)=4 which means that f(4)=-0.5 and I know that f(-0.5)=2 which means that f'(2)=-0.5, right? But I don't know how to relate this to tangent line approximation and find f(0). Can anyone explain this to me? Thanks!
    The derivative and the inverse function are two very different things. Linear approximation is as follows:

    $f(x+\Delta x) \approx f(x) + f'(x)\Delta x$

    In your case, $\Delta x = 0.5$
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    Re: Tangent line approximation help?

    Quote Originally Posted by SlipEternal View Post
    The derivative and the inverse function are two very different things. Linear approximation is as follows:

    $f(x+\Delta x) \approx f(x) + f'(x)\Delta x$

    In your case, $\Delta x = 0.5$
    So if it's f(x)+f'(x)delta(x) then that's 2+4(.5)=4 making f(0)=4?
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    Re: Tangent line approximation help?

    Quote Originally Posted by canyouhelp View Post
    So if it's f(x)+f'(x)delta(x) then that's 2+4(.5)=4 making f(0)=4?
    Not equal. Approximately equal. That is an approximation, not an exact answer. It is only equal if f(x) is a straight line. If it is a curve, it likely won't be accurate. 4 is the correct answer to the question.
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    Re: Tangent line approximation help?

    Quote Originally Posted by SlipEternal View Post
    Not equal. Approximately equal. That is an approximation, not an exact answer. It is only equal if f(x) is a straight line. If it is a curve, it likely won't be accurate. 4 is the correct answer to the question.
    Oh, okay, thank you!
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