Question

Find the equation of the tangent line to the curve at the given point.

y=1+2x−x3, (1,2)

Answer 1

so darkmare, are you there?

Answer 2

yes i am

Answer 3

so is this a calc marathon for u?:)

Answer 4

lets start with the derivative of a sum is the sum of the derivatives.

Answer 5

yup lol working on a bunch of hw problems trying to get them all figured out by tom, and it appears many of them are stumping me..... >.>

Answer 6

so do you have y'?

Answer 7

oh and apparently my typing skills arent so hot tonight either. the last term is x^3 not x3

Answer 8

ok. what is the derivative of 1 wrt x?

Answer 9

y' = 2-3x^2 correct?

Answer 10

you are batting a thousand! nice

Answer 11

how is y' related to the equation of the tangent line?

Answer 12

that would be equal to the slope of the line would it not?

Answer 13

it would! good again

Answer 14

oh! so my line would be y=-x+3 yes?

Answer 15

i was trying to find my slope by finding another coordinate... I didnt think to use y', which should have been my first thought being every question i'm dealing with is dealing with derivatives...

Answer 16

:). incidentally, the equation for your line is absolutely correct. :)

Answer 17

yay! lol i'm starting to understand this crazy calculus stuff..... kinda :P

Answer 18

you are doing fine.

Answer 19

k another question for you, the same deal i've got a function and a point and i'm looking for the line. How do i start off finding my derivative when the function is y= (2x)/((x+1)^2)

Answer 20

do I use chain rule on the bottom then quotient rule on the whole thing?

Answer 21

which do you like better, the quotient rule or the product rule?

Answer 22

deffinetly prefer the product rule

Answer 23

cuz you can rewrite that as y=2x(x+1)^-2

Answer 24

right then it would be a straight product rule

Answer 25

yes. cuz the stuff inside the parentheses has a derivative of 1. do you see that?

Answer 26

so no chain rule here :)

Answer 27

so then the derivative of (x+1)^-2 would be -2?

Answer 28

not quite. what is derivative of x^-2?

Answer 29

-2x^-3?

Answer 30

you bet. so the derivative of (x+1)^-2=?

Answer 31

-2(x+1)^-3?

Answer 32

yes!

Answer 33

so with my product rule then I get (2)(x+1)^-2 + (2x)(-2(x+1)^-3) Is that right so far?

Answer 34

yes... ! just clean up that last term and you are set. :)

Answer 35

how do I clean it up? i'm a little unsure of where to go from this step

Answer 36

in that term you have 2x times -2

Answer 37

so the second term is -4x(x+1)^-3. do you see that?

Answer 38

ya i can see that now that you pointed it out

Answer 39

it is just a matter of practice.. you will be fine.

Answer 40

does that mean my slope for my tangent line is 2(x+1)^-2 -4x(x+1)^-3?

Answer 41

I guess I was expecting my slope to be a whole number or fraction, so that's where i'm a little bit confused

Answer 42

are you given a point on the graph?

Answer 43

yes (0,0)

Answer 44

so what is y' at (0,0)?

Answer 45

2?

Answer 46

looks good to me :))

Answer 47

oh! lol wow I feel blonde, To find my slope I need to get my derivative and then plug in the x value of the point they give me

Answer 48

you look like you are starting to get it. :) that is exactly what i was going to write you. however, you came up with the correct solution strategy... :)

Answer 49

you should not feel blonde. you are doing fine.

Answer 50

Thank you soo much for your help! its clearing a lot of the fog in my head

Answer 51

glad to be of service. now, just out of curiosity...

Answer 52

is a darkmare worse or better than a nightmare?

Answer 53

:)

Answer 54

much much better :)

Answer 55

i bet. i hope you have a lovely evening (nite). you have this. do some more problems and you will nail this stuff :))

Answer 56

take care darkmare. :)

Answer 57

Thank you for all your help! :)

Answer 58

my pleasure... :)) nite