`f(x) = (x + 1)/(x - 1), ((1/2),-3)` Find an equation of the tangent line to the graph of `f` at the given point.

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Chapter 2, Review - Problem 43 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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`f(x) = (x+1)/(x-1)`

`f'(x) = [(x-1)*1 - (x+1)*1]/(x-1)^2`

`or, f'(x) = (-2)/(x-1)^2`

Now, slope of the tangent at point ((1/2),-3) = f'(1/2) = -8

Thus, equation of the tangent to the curve at the given point is :-

y + 3 = -8(x-(1/2))

or, y+3 = -8x + 4

or, y + 8x = 1  is the equation of the tangent to the curve

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