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Math Help - linear appx/graph reading

  1. #1
    Member cassiopeia1289's Avatar
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    linear appx/graph reading


    ok, I am completely at a loss - I don't even know where to begin.
    for (a): I should find the slope of T - but I have no idea how - could I make a triangle and solve for the hyp? so would it be like f'(a) = \sqrt{PQ^2 + QT^2}

    and then I am at a complete loss, partially because the given diagram is so confusing ... any help would be greatly welcomed
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  2. #2
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    Quote Originally Posted by cassiopeia1289 View Post

    ok, I am completely at a loss - I don't even know where to begin.
    for (a): I should find the slope of T - but I have no idea how - could I make a triangle and solve for the hyp? so would it be like f'(a) = \sqrt{PQ^2 + QT^2}

    and then I am at a complete loss, partially because the given diagram is so confusing ... any help would be greatly welcomed
    For a): The slope of the tangent line is equal to \frac{QT}{PQ}.

    For b): The value of the function is the length of the segment RS.
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  3. #3
    Member cassiopeia1289's Avatar
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    any hints as to how to answer c and d?
    those are where I am absolutely at a loss -
    c: I mean, would you find like {f(h) - f(a)}/(h-a)??
    and what are they even asking for d - and actual number?
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  4. #4
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    Quote Originally Posted by cassiopeia1289 View Post
    any hints as to how to answer c and d?
    those are where I am absolutely at a loss -
    c: I mean, would you find like {f(h) - f(a)}/(h-a)??
    and what are they even asking for d - and actual number?
    For part c, you use the tangent line at (a, f(a)) to approximate the value of the function at a + h. In the drawing you have, this approximation is given by the length of ST. But the formula for this approximation is y = f(a) + f'(a)(x - a), which simplifies to f(a) + f'(a)\cdot{h} in this case.

    For part d, this is simply \frac{f(a + h) - f(a)}{h}. It doesn't help you a whole lot except that as h approaches zero, this is the derivation of the derivative of f(x) at a.
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