Question

the equation of the line tangent to the curve y=kx+8/k+x at x= -2 is y=x+4. what is the value of k?

Answer 1

check your question , possibly a typo

Answer 2

no, thats it word for word

Answer 3

y= (k+1)x +(8/k) ( eqn of the "curve" , even though its a line )

Answer 4

the only way to have a tangent to a line , is for the tangent to be the line

Answer 5

so (k+1)x +(8/k) = x+4

Answer 6

now we are told they are a tangent at x=-2, so we could sub x=-2 into the above to find k , but we could also sub any value of x we like , these lines have to be the same for all x

Answer 7

but ill just sub x=-2

-2(k+1) + 8/k = 2

-2k(k+1) +8 = 2k
-2k^2 -2k -2k +8 =0
-2k^2 -4k+8 =0

-2(k^2 +2k -4) =0

Answer 8

k^2 +2k -4 =0

Answer 9

how did you get that function?

Answer 10

(k+1)^2 = 5
k +1 = +-sqrt(5)

k = -1+-sqrt(5)

Answer 11

not an answer

Answer 12

well your teacher is stupid

Answer 13

i doubt that you dont even know what the equation of the line tangent is

Answer 14

this is a question from an ap test so there are no typos

Answer 15

lol

was the curve

\[y=kx + \frac{8}{k+x}\]

y =

Answer 16

if it was................ :|

Answer 17

use brackets when you are writting fractions on the net :|

Answer 18

put the kx on top also

Answer 19

sorry? didnt know

Answer 20

lol

Answer 21

y=(kx+8)/k+x

Answer 22

With the given info, one finds the tangent vector of the curve to be <1, -1> and the point of tangency to be (-2, 2). You can find k by plugging in (-2, 2).