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Math Help - General ?: Given f'(x) or f''(x) Sketch f(x)

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    General ?: Given f'(x) or f''(x) Sketch f(x)

    Just in general. I was just wanting some steps on how I should go about sketching f(x)...

    I know that Integration is the area of the curves...

    Thanks!

    -qbkr21
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    Quote Originally Posted by qbkr21 View Post
    Just in general. I was just wanting some steps on how I should go about sketching f(x)...

    I know that Integration is the area of the curves...

    Thanks!

    -qbkr21
    we could use integration, but we don't have to

    this is similar to those "fully analyse the curve" questions, except we go a bit backwards.

    given f ' (x) and f '' (x) we can find:
    max and mins
    concavity
    intervals of increase and decrease

    with that information we can tell exactly what f(x) will look like
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    Re:

    RE:

    I know but I was just thinking more in general...

    Suppose the the graph below is of f''(x) what would f(x) look like since there is no function given to us?

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    Quote Originally Posted by qbkr21 View Post
    RE:

    I know but I was just thinking more in general...

    Suppose the the graph below is of f''(x) what would f(x) look like since there is no function given to us?

    in general, we know that a graph of x^n where smaller powers of x are accounted for will have n-1 turns and n roots.

    so a graph of y = ax^5 + bx^4 + cx^3 + dx^2 + ex + d will in general, have 5 roots and 4 turns

    now the derivative cuts down one power, so for a general x^5 graph, f ' (x) would look like a general x^4 and f '' (x) would look like an x^3 graph.

    the above example looks like an x^3 graph, so we expect f ' (x) to look like an x^4 graph and f(x) to look like an x^5 graph. we can get the specific graph by doing some analysis, but you said in general, so let's not do that now...unless you want to. it would be a pain, since such questions never ask you for specific graphs, i dont think
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    Re:

    This whole thing pertains to stupid questions on the final about local extrema's. I figured I could bake the section if I just drew up a graph of f(x) of off their f''(x).
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    if you are inclined to examine this question further, i can start you off by saying this. the graph of f '' (x) cuts the x-axis at -2, 2 and 4. so these are the points where the second derivative is zero, and thus these are the possible inflection points. that's the first peice of important info. we can construct the formula for this graph without even using calculus. since it's a general x^3 graph with roots -2, 2 and 4, we know it will be the graph where

    y = (x + 2)(x - 2)(x - 4)

    expand that and you have the graph of f '' (x).
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    Quote Originally Posted by qbkr21 View Post
    This whole thing pertains to stupid questions on the final about local extrema's. I figured I could bake the section if I just drew up a graph of f(x) of off their f''(x).
    ok, well i hope my posts helped you accomplish that
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    Re:

    Jhevon thanks again for the help I think that I have an accurate graph now...

    Consider...
    Attached Thumbnails Attached Thumbnails General ?: Given f'(x) or f''(x)  Sketch f(x)-sketch-backwards.gif  
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    Quote Originally Posted by qbkr21 View Post
    Jhevon thanks again for the help I think that I have an accurate graph now...

    Consider...
    well, those probably aren't completely accurate. remember when intergrating we obtain an aribitrary constant.

    so f ' (x) = (1/4)x^4 - (4/3)x^3 - 2x^2 + 16x + C
    and f(x) = (1/20)x^5 - (1/3)x^4 - (2/3)x^3 + 8x^2 + Cx + D

    your functions will only be accurate if constants C and D are zero, and innaccurate otherwise
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    Re:

    Ohhh...Yea I forgot always add a +/- C +/-D...My bad; is there anyway or formula that would give them to me under these conditions?

    Possibly Local/Relative Extrema's; Inflection Points?

    -qbkr21
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    Quote Originally Posted by qbkr21 View Post
    Ohhh...Yea I forgot always add a +/- C +/-D...My bad; is there anyway or formula that would give them to me under these conditions?

    Possibly Local/Relative Extrema's; Inflection Points?

    -qbkr21
    i don't recall any methods or formula's that would give you the exact graphs at the moment. we'd probably need more clues
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    Re:

    Ok Thanks Man I appreciate the help!
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