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

by A_Munk3y
Tags: equation, function, graph, line, tangent
 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.
 HW Helper Sci Advisor Thanks P: 24,454 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.
 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
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?
HW Helper
Thanks
P: 24,454
 Quote by A_Munk3y ... 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?
 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.
 PF Patron P: 1,930 Why would you implicitly differentiate? Since 3 is an odd power, you can solve for y without losing any information...
HW Helper