Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

Find the difference quotient of​ f; that is,  find f(x+h)-f(x) / h  ,h ≠ 0 .  Be sure to simplify.?

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  • ?
    Lv 7
    8 months ago

    See below for work and answer:

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  • 8 months ago

    You have:

    f(x) = x² - 9x + 2

    And asked to solve for:

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

    We have f(x) already, so we need to find f(x + h):

    f(x) = x² - 9x + 2

    f(x + h) = (x + h)² - 9(x + h) + 2

    Simplify:

    f(x + h) = x² + 2hx + h² - 9x - 9h + 2

    Now we can substitute both expressions into the main expression and simplify:

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

    [(x² + 2hx + h² - 9x - 9h + 2) - (x² - 9x + 2)] / h

    (x² + 2hx + h² - 9x - 9h + 2 - x² + 9x - 2) / h

    Cancel out what can be:

    (2hx + h² - 9h) / h

    Factor out the h and cancel with the denominator:

    h(2x + h - 9) / h

    2x + h - 9

  • 8 months ago

    Ted was doing well until he (mis)typed 2x - 6 + h.

    He meant 2x - 9 + h.

  • ted s
    Lv 7
    8 months ago

    ( x + h)² - x² - ( 9x + 9h - 9 x ) + ( 2 - 2 ) = 2 h x + h² - 9 h = h [ 2x + h - 9 ] ===> answer is  2x - 6 + h

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