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Math Help - functions & simplifying

  1. #1
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    functions & simplifying

    Let f(x) = 5x^3 - 6x^2 + 3.

    Simplify:

    [f(x+h) - f(x-h)] / 2h



    Thanks.
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  2. #2
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    Corrected solution

    Hello, Mr_Green!

    Let f(x) = 5x - 6x + 3

    Simplify: .[f(x+h) - f(x-h)] / 2h

    Don't be intimidated by a "difference quotient".

    There are four separate steps to perform:
    . . (1) Find f(x+h) . . . and simplify
    . . (2) Find f(x-h) . . . and simplify
    . . (3) Subtract (2) from (1)
    . . (3) Divide by 2h . . . and simplify


    (1) f(x+h) .= .5(x+h) - 6(x+h) + 3
    . . . . . . . . = .5(x + 3xh + 3xh + h) - 6(x + 2xh + h) + 3
    . . . . . . . . = .5x + 15xh + 15xh + 5h - 6x - 12xh - 6h + 3

    (2) f(x-h) .= .5(h-h)3 - 6(x-h)2 + 3
    . . . . . . . = .5(x - 3xh + 3xh - h) - 6(x - 2xh + h) + 3
    . . . . . . . =5x - 15xh + 15xh - 5h - 6x + 12xh - 6h + 3

    (3) f(x+h) - f(x-h) .= .5x + 15xh + 15xh + 5h - 6x - 12xh - 6h + 3)
    . . . . . . . . . . . . . . . - (5x -15xh + 15xh - 5h - 6x + 12xh - 6h + 3)
    = .5x + 15xh + 15xh + 5h - 6x - 12xh - 6h + 3 - 5x + 15xh - 15xh + 5h + 6x - 12xh + 6h - 3
    = .30xh + 10h - 24xh


    . . . f(x+h) - f(x) . . . .30xh + 10h - 24xh
    (4) --------------- . = . -------------------------
    . . . . . . 2h . . . . . . . . . . . . .2h

    . . . . . . . . . . . . . . .2h(15x + 5h - 12x)
    Factor and reduce: . --------------------------
    . . . . . . . . . . . . . . . . . . . . 2h


    Answer: . 15x + 5h - 12x

    Last edited by Soroban; February 11th 2007 at 07:41 PM.
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  3. #3
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    wouldn't u subtract f(x-h) not just f(x)????????
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  4. #4
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    Quote Originally Posted by Mr_Green View Post
    wouldn't u subtract f(x-h) not just f(x)????????
    Yes, you would. His method is correct other than on this point, so you've got the method at least. In his defense Soroban's error was a very easy mistake to make since the first derivative in Calculus is defined in a very similar way.

    -Dan
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  5. #5
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    Yes . . . a really stupid error!

    I've corrected it . . . Sorry for the confusion.
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