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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?
how did you simplify the numerator, ((3/x)-(3/4) ?
I made it 12-3x all over 4x.
yes, 12-3x = 3 (4-x) right ? = -3 (x-4) and did you cancel out x-4 then ?
Yup, i was left with -3/4x.
The extra x is messing it up i guess?
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)
Woh wait where are you getting -4? Why do i plug that in for x??
like lim x->a f(x) = f(a) we substitute x=a here it'll be -3/4(-4)
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
lim x->4 -3/4x = -3/4(4)
So its -3/16? I thought the x-4's both canceled out, so why do we use that for x?
Oh *facepalms* i see now.
Forgot about P(4,3/4)
yes, -3/16 as i said, we need derivative at point P, whose x-coordinate is 4....
Alright, so then the equation for the tangent line at P would be y-4=-3/16 (x-3/4)
Still need to simplify of couse.
y-y1 = m (x-x1) i think you interchanged x and y
y-3/4 = -3/16 (x-4) isn't it?
Oh my bad. So it should end up as y=-3/16x +3/2
Thanks again : )