Expert: Bobby Soltani - 6/17/2005

Question
I'm not sure how to set this up.  I think that if I had a good example, I could follow it, but I can't find a good example. ;-)  Anyhow:
y = 1 - 2x -3x^2.   (-2, -7) is the point.
find the equation of the tangent line to the given curve at the given point.

Answer
Hi Devon,

To get the equation for a line, you need a slope and a point.  We are already given the point (-2,-7).  To find the slope of the tangent, we need to take the derivative of the equation and evaluate it at x = -2.

f(x) = 1 - 2x - 3x^2

f'(x) = -2 - 6x

f'(-2)= -2 - 6(-2)

= 10

So we can write the eqauation for the line with slope m = 10 and point (x1,y1) = (-2,-7) as,

(y-y1)=m(x-x1)

Let me know if you have any questions.

Bobby