Well, I guess it's more like an algebra problem since I understand the calc just fine.
I need to find an equation of the tangent line to the curve at the given point:
y = 1 + 2x - x^3 @ P(1 , 2)
To do this, I first need to find the slope with the following method: (f(x) - f(a)) / (x - a)
( (1 + 2x - x^3) - (2) ) / (x - 1)
becomes..
(2x - x^3 - 1) / (x - 1)
Top and bottom equal 0 if you plug in 1, so that means there's a way to factor them even further, correct? Meaning... (x + 1) * (?) = 2x - x^3 - 1 ?
The book says the answer is y = -x + 3, but I can't even get past simplifying (2x - x^3 - 1) / (x - 1) to get the slope.
Does x - 1 factor out of the numerator, or am I going about this all wrong?
Thanks for the help
