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# 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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- MyRankLv 61 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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- PuzzlingLv 71 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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