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Math Help - AP Exam Practice Packet : Free Response

  1. #1
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    AP Exam Practice Packet : Free Response

    i cant seem to understand this concept, its very confusing, can anyone give me any tips?

    4. Suppose that the function f has a continuous second derivative for all x, and that f(0)=2, f'(o)=-3, and f''(0)=0. Let g be a function whose derivative is given by g'(x)=e^{-2x} (3f(x)+2f'(x)) for all x.

    a. Write an equation of the line tangent to the graph of the f at the point where x=0
    b. Is there sufficient information to determine whether or not the graph of f has a point of inflection when x=0? Explain your answer.
    c. Given that g(0)=4, write an equation of the line tangent to the graph of g at the point where x=0
    d. Show that g''(x)=e^{-2x} (-6f(x)-f'(x)+2f''(x)). Does g have the local maximum at x=0? Justify your answer.

    Some help would very much be appreciated.
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  2. #2
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    Quote Originally Posted by DarkestEvil View Post
    i cant seem to understand this concept, its very confusing, can anyone give me any tips?

    4. Suppose that the function f has a continuous second derivative for all x, and that f(0)=2, f'(o)=-3, and f''(0)=0. Let g be a function whose derivative is given by g'(x)=e^{-2x} (3f(x)+2f'(x)) for all x.

    a. Write an equation of the line tangent to the graph of the f at the point where x=0

    they gave you everything you need to do that ... f(0) = 2 and f'(0) = -3

    b. Is there sufficient information to determine whether or not the graph of f has a point of inflection when x=0? Explain your answer.

    what do you need to tell you that f(x) has inflection point(s) ?


    c. Given that g(0)=4, write an equation of the line tangent to the graph of g at the point where x=0

    another tangent line problem ... they gave you the point, g(0) = 4 , all you need is the value of g'(0) for the slope of the line ... can you find that?

    d. Show that g''(x)=e^{-2x} (-6f(x)-f'(x)+2f''(x)). Does g have the local maximum at x=0? Justify your answer.

    fairly straightforward ... they gave you g'(x) and want you to find g''(x) simplified to the given form.
    ...
    Last edited by skeeter; March 18th 2010 at 06:15 PM. Reason: fix typo
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    Quote Originally Posted by skeeter View Post
    ...
    a. But how would I take the derivative if I don't know f(x)? How do I use g'(x) to do this?
    b. I know to find these, I must take the second derivative of f(x), and set it equal to zero, find the x-values, and plug them into f(x) to get the y-value for the points.
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    Quote Originally Posted by skeeter View Post
    c. Given that , write an equation of the line tangent to the graph of at the point where

    another tangent line problem ... they gave you the point, g(0) = 4 , all you need is the value of g'(4) for the slope of the line ... can you find that?
    Why would the slope of the line tangent to g at x=0 be g'(4)?
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  5. #5
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    Quote Originally Posted by ione View Post
    Why would the slope of the line tangent to g at x=0 be g'(4)?
    my mistake ... g'(0)
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    I don't see where you're getting at, how do I use g'(x) in order to differentiate f(x)?
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  7. #7
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    Quote Originally Posted by DarkestEvil View Post
    I don't see where you're getting at, how do I use g'(x) in order to differentiate f(x)?
    You do not need to differentiate f(x) because you are given that
    f'(0)=-3
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