Question

Find an equation of the tangent line to the given curve at this point
1. y= 1 + 2x - x^3 (1,2)

Answer 1

find y'
it tells you the slope of the function for any x.
the slope of the function at x=1 will be y ' (1)
so that will also be the slope of the tangent line at that point.
you now have 'm' in ' y=mx+b'
use the point x=1 and y=2 to find the value of 'b'

Answer 2

i still dont understand.. thats not what my teacher taught. we need to find the slope some how byt using f(x)-f(a)/x-a

Answer 3

ok, so you haven't learned rules of differentiation yet?

Answer 4

no not yet

Answer 5

\[\lim_{a \rightarrow0} \frac{1 + 2x - x^3 -(1 + 2a - a^3)}{ x-a }\]

Answer 6

\[\lim_{a \rightarrow0} \frac{ 2x - x^3 - 2a +a^3}{ x-a }\]

Answer 7

\[\lim_{a \rightarrow0} \frac{ -(x^3 -a^3) + 2x- 2a }{ x-a }\]

Answer 8

use the difference of cubes formula on (x^3 -a^3)
\[a^3 – b^3 = (a – b)(a^2 + ab + b^2)\]

Answer 9

\[\lim_{a \rightarrow x} \frac{ - (x – a)(x^2 + ax +a^2) +2(x-a)) }{(x-a) }\]

Answer 10

I had a->0 in those earlier limits, it's supposed to be a->x

Answer 11

need me to retype them or is it ok?

Answer 12

no your fine i understand so far

Answer 13

that's about it really... (x-a) is in both terms in the numerator and also in the denominator. cancel it.
then take the limit...

Answer 14

so you get (a^2 + ax + x^2 ) + 2

Answer 15

yep:)

Answer 16

but that isnt an equation

Answer 17

take the limit.

Answer 18

what do you mean take the limit the limit for that

Answer 19

we're finding the derivative here, remember? that's step one. once you have the derivative you have the slope of the function for any x...

find y'
it tells you the slope of the function for any x.
the slope of the function at x=1 will be y ' (1)
so that will also be the slope of the tangent line at that point.
you now have 'm' in ' y=mx+b'
use the point x=1 and y=2 to find the value of 'b'

Answer 20

it never says x is one in my problem though

Answer 21

"at this point (1,2)"

Answer 22

so why did i just do all that work if i can just plug in 1 in the first place

Answer 23

go for it.

Answer 24

but i just really dont understand what the hell im doing your telling me i can do so many different things. like wtf

Answer 25

why don't you show me how you'd do the problem.

Answer 26

i dont know thats the problem thats why i came on here

Answer 27

And I just showed you.

Answer 28

but you don't seem to like it; you have an easier way. so show me.

Answer 29

im asking you i dont know what to do! none of this makes sense to me, i understnand it all in class and then when it comes to homework i sit for hours and not know what im doing like its to the point where im cying

Answer 30

do you understand that the tangent line at a point has the same slope as the function at that point?

Answer 31

nevermind forget thank you. ill just ask my teacher tomorrow.

Answer 32

k.

Answer 33

no need to be a fluttering feather i said thank you.

Answer 34

blocked.

Answer 35

lol bye (: