A few days ago
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
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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)
so
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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