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Math Help - f(x + h) -f(x)/h ......can someone please show me the steps and answer to this

  1. #1
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    Question f(x + h) -f(x)/h ......can someone please show me the steps and answer to this

    Find f(x+h) - f(x) for f(x) = x (squared) +5x - 1
    h
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  2. #2
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    Hello, wayneo1688!

    I assume you're new to the Difference Quotient.


    Find \frac{f(x+h) - f(x)}{h} . for . f(x) \:= \:x^2 +5x - 1
    Don't let the Difference Quotient scare you.
    . . Break it down into its three basic steps.

    (1) Find f(x+h) . . . Replace x with x+h ... and simplify.

    (2) Subtract f(x) . . . Subtract the original function ... and simplify.

    (3) Divide by h . . . Factor and cancel (carefully!)



    Here we go! . . . We have: . f(x)\:=\:x^2 +5x - 1

    (1)\;\;f(x+h) \;=\;(x+h)^2 + 5(x+h) - 1 \;=\;x^2 + 2xh + h^2 + 5x + 5h - 1

    (2)\;\;f(x+h) - f(x) \;=\;(x^2 + 2xh + h^2 _ 5x + 5h - 1) - (x^2 + 5x-1) \;=\;2xh + h^2 + 5h

    (3)\;\;\frac{f(x+h)-f(x)}{h}\;=\;\frac{2xh + h^2 + 5h}{h} \;=\;\frac{\not{h\;}(2x + h + 5)}{\not{h\:}} \;=\;{\color{blue}2x + h + 5}

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  3. #3
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    I know this was posted a very long time ago, but stumbled across it trying to solve my calculus homework and wanted to say it is very inciteful and informative. Thanks!
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