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Math Help - Just 2 questions

  1. #1
    Junior Member
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    Just 2 questions

    sorry to ask for so much help

    they ask me to find the average rate of change from x=1 to x=2 in the equation x-2x^2

    then they give me the equation x^2-2 and ask me to find f(x+h)-f(x)/h

    thank you.
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  2. #2
    Super Member

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    Hello, jhonwashington!

    Find the average rate of the function: .f(x) .= .x - 2x from x=1 to x=2.
    . . . . . . . . . . . . . . . . . . . . . . . . . change in f(x)
    Average rate of change of f(x) . = . -----------------
    . . . . . . . . . . . . . . . . . . . . . . . . . .change in x


    We have: . f(1) .= .1 - 2(1) .= .-1
    . . . .and: . f(2) .= .2 - 2(2) .= .-6
    The change in f(x) is: .(-6) - (-1) .= .-5

    The change in x is: .2 - 1 .= .1

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -5
    Therefore, average rate of change of f(x): . -- . = . -5
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1



    Given: .f(x) .= .x - 2

    . . . . f(x + h) - f(x)
    Find -----------------
    . . . . . . . . h

    There are three steps to this "difference quotient":
    . . (1) Find f(x + h) ... and simplify
    . . (2) Subtract f(x) ... and simplify
    . . (3) Divide by h ... and simplify


    We have:

    (1) f(x+h) .= .(x+h) - 2 .= .x + 2xh + h - 2

    (2) f(x+h) - f(x) .= .(x + 2xh + h - 2) - (x - 2) .= .2xh + h

    . . .f(x+h) - f(x) . . .2xh + h . . h(2x + h)
    (3) -------------- .= .---------- .= .----------- .= .2x + h
    . . . . . . h . . . . . . . . . h . . . . . . . .h

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