Slope of the tangent line

metalmagik

1. The problem statement, all variables and given/known data
Find the slope of the tangent line to the curve y=x³ at point (-1,-1)
(i) Using Definition 1
m=lim_x-->a[tex]\frac{f(x)-f(a)}{x-a}[/tex]

(i) Using Equation 2
m=lim_h-->0[tex]\frac{f(a+h)-f(a)}{h}[/tex]


2. Relevant equations



3. The attempt at a solution
For the first one, I got as far as lim_x-->-1x³+1/x+1 and was stuck. I thought it was undefined. Then I plugged it into a limit calculator online in desperation, and found that the answer was 3. But for equation 2 I got to the end and go undefined again, plugged it into the limit calculator seeing that it said it was undefined too. I just wanna know how you would go about completing the first one, and I am just a little confused at the point of this exercise. Thanks for any help you guys can give me.

foxjwill

for the first one, try factoring numerator. You should find that things cancel out. And by the way, it's not undefined, it's in an "indeterminate form". And for the second one, expand the numerator, and again, you'll find that things cancel out. :)

metalmagik

how do I factor x³+1...its not (x+1)³

sutupidmath

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]