Question

Find the equation of both tangent lines to f(x)..

Answer 1

\[\LARGE f(x)=\frac{x+1}{x-1}\] that are parallel to 2x+y=7

Answer 2

f'(x)=-2

Answer 3

I don't even understand the question, equation TO both tangent lines??

Answer 4

I knew the slope was -2. And whoops, that's suppose to say "of" not "to"

Answer 5

Just don't know where to go from there.

Answer 6

set f'(x) = -2

Answer 7

there should be two values of x after differentiating f(x)

Answer 8

Hmm
\[\LARGE =\frac{(x-1)(1)-(1)(x+1)}{(x-1)^2}\]
\[\LARGE f'(x)=\frac{-2}{(x-1)^2}\]

Answer 9

@Luigi0210
Can you find the points on the curve y = f(x) for whom the f'(x) = (-2) ??

Answer 10

(2,3), (0,-1)
these are the points where f'(x)=-2

Answer 11

Now, we only have to write the equation for each straight line using point-slope form..

Answer 12

So..
\[\LARGE y-3=-2(x-2)\]
\[\LARGE y+1=-2(x-0)\]
------------------------------
\[\LARGE y=-2x+7\]
\[\LARGE y=-2x-1\]

Answer 13

But how did he find those two points? Just by setting the derv =-2?

Answer 14

f'(x) = -2
will give you two values of x (lets say x_1 & x_2)

Then y_1 = f(x_1)
& y_2 = f(x_2)

Answer 15

the x-coordinate are found by setting f'(x) = 2

the y-coordinate are found by plugging those x's in f(x)

Answer 16

Alright, makes sense, thanks guys :)

Answer 17

You're welcome :)