how do you solve for  Find f′(2) for f(x) = ln(2x^2 − 8x + 7) rounded to 3 decimal places?

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  • MyRank
    Lv 6
    1 month ago

    f(x) = ln (2x² - 8x + 7)

    f′ (2) =?

    Differentiation with respect to x

    f’(x) = 1/ (2x² - 8x + 7) d/dx (2x² - 8x + 7)

    = 1/ (2x² - 8x + 7) (4x – 8 + 0)

    = (4x – 8)/(2x^2 -8x + 7)

    f′ (2) = (4(2) – 8)/(2(2)^2 -8(2) + 7)

    f′ (2) = 0

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  • alex
    Lv 7
    1 month ago

    rule:

    f(x) = ln(g(x)) ---> f '(x) = g'(x)/g(x)

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  • 1 month ago

    Use the chain rule to take the derivative.

    f(x) = ln(u), u = 2x² - 8x + 7

    f'(x) = 1/u * d/dx(u)

    = 1/(2x² - 8x + 7) * (4x - 8)

    = (4x - 8) / (2x² - 8x + 7)

    Then just plug in x=2.

    f'(2) = (4*2 - 8) / (2*2² - 8(2) + 7)

    = 0 / -1

    = 0

    Answer:

    0

    Update:

    In rechecking this, at x=2, you'd be trying to take the log of a negative number.

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  • 1 month ago

    mayybe you can read your notes and boook

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