Question

let f(x) be defined as f(x)=1+2x-x^3. Find the equation of the line tangent to f(x) in slope-interecpt form at the point where x=1

Answer 1

f'(x) = 2-3x

m = 2-3(1)
= -1

y = 1 + 2(1) - (1)^3 = 2
(1,2)

Tangent: m = -1
y - y^1 = m (x-x^1)
y - 2 = -1(x-1)
y - 2 = -x + 1
T: x - y -3 = 0
Like that ? xD

Answer 2

i think your answer is right, but the derivative is
\[f'(x)=2-3x^2\]

Answer 3

Woops , but it's right anyway since x is 1

Answer 4

LOL

Answer 5

Shut up xD
People makes mistakes that was a typo :P

Answer 6

i know it was a typo. i make them all the time.

Answer 7

can u tell what step goes first, and thereafter

Answer 8

Hm , Saifoo can explain :P

Answer 9

lol, im learning that.. i learned some of it yesterday

Answer 10

Learning it!? Yeah right, I thought you passed HS?

Answer 11

HS here is a bit different. :P

Answer 12

we pass HS in 10th. then study 2 years college after it.

Answer 13

wow~ in yr 10!? :O:O
So yr 11 and 12 is college there ?

Answer 14

oh yes this is very helpful <_< lol nevermind. i found my notes. this is too easy lol

Answer 15

LOL, sorry need me to elaborate ?

Answer 16

if u dont mind

Answer 17

yessss!!

Answer 18

so the final answer should be -1x+3 right?

Answer 19

Okay since Saifoo can't help :P

First you have to find the derivative then it's f'(x) = 2 - 3x^2
Then you have to find the gradient using x = 1 , f'(x) = 2 - 3(1)^2
m = -1
Oh yeah then find the y by substituting x into the thing y = 1 + 2(1) -(1)^3 = 2

Tangent:
(x1, y1) = (1,2)
y - y1 = m(x-x1)
y - 2 = -1(x-1)
y - 2 = -x + 1
T; x - y -3 = 0

Answer 20

y = x - 3 , if its not in general form

Answer 21

hold on i got -1x+3

Answer 22

y=m(x-x1)+y
-1(x-1)+2

Answer 23

what? I don't get yur way

Answer 24

well my way is basically ur way except i add y to the other side. and when siimplified it should be -x+3, your doing something wrong

Answer 25

T; x - y -3 = 0 where does this come from?

Answer 26

I doubled check, nothing is wrong =/

Answer 27

Oh, we did it in different forms, your answer is right, my answer is right as well

Answer 28

ok thx

Answer 29

yw (:

Answer 30

I did do a stupid mistake sorry =/
T: x+y-3 = 0