Question

Slope of a tangent line of graph at P

Answer 1

So far i had ((3/x)-(3/4)) divided by (x-4). I simplified that out to -3/4x for the slope but that was incorrect. Am i approaching it wrong?

Answer 2

how did you simplify the numerator, ((3/x)-(3/4) ?

Answer 3

I made it 12-3x all over 4x.

Answer 4

yes,
12-3x = 3 (4-x)
right ?
= -3 (x-4)
and did you cancel out x-4 then ?

Answer 5

Yup, i was left with -3/4x.

Answer 6

The extra x is messing it up i guess?

Answer 7

i see, you did
so, you have
limit x=>-4 -3/4x
not just
-3/4x
you need to substitute x= -4 in
limit x=>-4 (-3/4x)

Answer 8

Woh wait where are you getting -4? Why do i plug that in for x??

Answer 9

like lim x->a f(x) = f(a)
we substitute x=a
here it'll be
-3/4(-4)

Answer 10

the limit is x->a
we are taking the limit AT POINT P
and x-co-ordinate at P is 4
ohh...its 4 , not -4 :P sorry

Answer 11

lim x->4 -3/4x = -3/4(4)

Answer 12

So its -3/16? I thought the x-4's both canceled out, so why do we use that for x?

Answer 13

Oh *facepalms* i see now.

Answer 14

Forgot about P(4,3/4)

Answer 15

yes, -3/16
as i said, we need derivative at point P, whose x-coordinate is 4....

Answer 16

Alright, so then the equation for the tangent line at P would be y-4=-3/16 (x-3/4)

Answer 17

Still need to simplify of couse.

Answer 18

y-y1 = m (x-x1)
i think you interchanged x and y

Answer 19

y-3/4 = -3/16 (x-4)
isn't it?

Answer 20

Oh my bad. So it should end up as y=-3/16x +3/2

Answer 21

yes. :)

Answer 22

Thanks again : )

Answer 23

welcome ^_^