A few days ago

Amber P

Find equations of the tangent lines to the curve below that are parallel to the line x – 2y = 2.?

y= (x-1)/(x+1)

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

x – 2y = 2

gives

y = (1/2)x – 1

so the gradient of the line is 1/2

then

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

f'(x) = 2/(x+1)^2 by the product rule

so if f'(x) = 1/2

2/(x+1)^2 = 1/2

(x+1)^2 = 4

x+1 = ±√4 = ±2

x = ±2 – 1 = -3 and 1

then

f(-3) = 2 and f(1) = 0

so the points where the gradient is parallel to the line are

(xo, yo)= (-3, 2) and (1, 0)

substitute these points in to the point gradient formula

y – yo = (1/2)*(x – xo)

to find the two lines

y – 2 = (1/2)*(x +3)

and

y = (1/2)*(x – 1)

just expand these out and your done

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