Edwin W.

asked • 02/28/23

Equation of a tangent line

Inactive Tutor

Edwin, are you able to find the derivative using the quotient rule, or is that where you are stuck?
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02/28/23

Inactive Tutor

OK, here is a Desmos graph confirming the answer from Jesus: desmos.com/calculator/j4rsrpwlzn You can slide point T to various locations to see additional tangent lines.
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02/28/23

1 Expert Answer

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Inactive Tutor answered • 02/28/23

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Let f(x) = 2x/(x-1)


Use quotient rule to find f'(x) = [(x-1)(2) - (2x)(1)] / (x-1)2

Plug in x=-1 to find f'(-1) = [(-1-1)(2) - (2*-1)(1)] / (-1-1)2

So f'(-1) = [-4-(-2)]/(-2)2

f'(-1) = -2/4= -1/2


We now use the point-slope form equation: y-y1 = m(x-x1)

So then we have y-1 = -1/2(x+1) using point slope form and m=f'(-1)

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