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

do you know the answer?

Answer 2

i feel like its 1

Answer 3

okay, i just check and i know now,


we have an equation where the k does not play into account, that is the equation of the tangent,

what do we know of the tangent? is that at point(x,y) which in this case (-2,y) we have an tangent for y=kx+8/k+x

so

using the equation of the tangent we can work out y which is y=-2+4 = 2


so we have (-2,2)

now, we have two knowns and 1 unknown in the original equation of the curve,

if we plug these in we get


y=(-2k+8)/(k-2)=2 we know that x=-2

==>

-2k+8=2k-4

==>

12=4k

==>

k=3

Answer 4

do you understand?

Answer 5

look at picture,

red line is the line of the tangent

where they touch is (-2,2)

the blue line is the original equation but with k=3,


so this is correct

Answer 6

yes thank you! i dropped a negative sign so it didnt make sense! thank you your explenation was very helpfull!

Answer 7

yw