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Find an equation of the tangent line to the graph of the function f

by A_Munk3y
Tags: equation, function, graph, line, tangent
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A_Munk3y
#1
Sep29-10, 05:03 PM
P: 72
1. The problem statement, all variables and given/known data
Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point.
(x - y - 1)3 = x; (1, -1)



3. The attempt at a solution
x3-y3=1
3y2(dy/dx)-3x2=0
3y2(dy/dx)=3x22
(dy/dx)=3y2/3x2
(dy/dx)=x2/y2
slope = (dy/dx) = 1

y-(-1)= 1(x-1)
y=x-2

thats wrong -.-
i tried making it dy/dx = x/y and still wrong.
where am i messing up? I'm pretty sure it has to do with the x at the end but i have no idea what to do with it!
We just learned derivatives so I'm still messing up with them.
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Dick
#2
Sep29-10, 05:08 PM
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What has x^3-y^3=1 got to do with the problem? Your equation is (x-y-1)^3=x. Find y' using implicit differentiation.
A_Munk3y
#3
Sep29-10, 05:17 PM
P: 72
Yea, i thought i was deriving it wrong :) Ok, let me go back and look at my notes to see how to do implicit differentiation.
Thanks

A_Munk3y
#4
Sep29-10, 05:49 PM
P: 72
Find an equation of the tangent line to the graph of the function f

... i can't figure out how to do the implicit differentiation on this. Could someone help me out with it?
Dick
#5
Sep29-10, 05:53 PM
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Quote Quote by A_Munk3y View Post
... i can't figure out how to do the implicit differentiation on this. Could someone help me out with it?
The derivative of u^3 is 3*u^2*u'. Put u=x-y-1. What do you get? Is that the part that's confusing you?
A_Munk3y
#6
Sep29-10, 06:02 PM
P: 72
I'm getting confused on the dx/dy part. I'm not even sure i understand how to do this right.
I thought i had to have them all cubed then get the derivative of x3-y3-13 but obviously that's not right since your first response was what did x3-y3= 1 have to do anything.

So is it 3x2*u and 3y2*u -1? and then i add the dx/dy part somewhere? Or am i just way off here :(
Sorry, we just learned this stuff today and it still hasn't really sunk in.
Char. Limit
#7
Sep29-10, 07:23 PM
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Why would you implicitly differentiate? Since 3 is an odd power, you can solve for y without losing any information...
Dick
#8
Sep29-10, 08:53 PM
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Quote Quote by Char. Limit View Post
Why would you implicitly differentiate? Since 3 is an odd power, you can solve for y without losing any information...
Good point. If you aren't comfortable with implicit differentiation, try it that way. They both work.


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