Question

How do I find the equation of the tangent line to f at the point (-3,4)?
f(x)= x^2 +2x +1
Derivative and the limit process problem!

Answer 1

1. Find the derivative of f(x)
2. Plug in your x-value to your derivative to get the slope your tangent line needs to have...m
3. Use the point slope equation to get the equation of your tangent line.
y - y1 = m (x - x1)
m is your slope from part 2......x1 and y1 can be the point given in the problem

Answer 2

ok, so I have tried to find the derivative a few times already, but i'm not sure i'm doing it correctly:
lim deltax->0 f(x+deltax) -f(x)/deltax
I put in (x+deltax)^2 +2(x+deltax) +1 -(x^2+2x+1)/deltax
(x+deltax)(x+deltax) +2x +2deltax +1 -x^2 -2x -1/deltax
x^2 +xdeltax +xdeltax +x^2 +2deltax -x^2/deltax
2xdeltax +deltax^2 +2deltax
deltax(2x +deltax+2)/deltax
2x+deltax+2 sub in 0
f'(x)= 2x+2???
Is this correct for the derivative?

Answer 3

but when I substitute in the point or graph it on my calculator, I get (-3,-4) so I must be doing something wrong? The line crosses the parabola at (-3,-4) instead of (3,4) when I graph it...

Answer 4

I figured it out! The equation is y= -4x -8!