Need help with tangent lines and derivatives

Hey,

I'm struggling with this one problem from my text book.

"Find the equations of the tangent lines to the parabola y=(x^2)+x that pass through the point (2, -3)."

I know how to find the derivative (2x+1) and then I can find one set of points (5,30) but I can't figure out how to find the other set of points.

Thanks for your help!

Re: Need help with tangent lines and derivatives

f'(a) = 2a + 1

And the slope of the line between the point (a, a^2 + a) and (2, -3) is (a^2 + a + 3)/(2 - a) = 2a + 1

Can you solve that?

Re: Need help with tangent lines and derivatives

Yes, I get the points (5, 30) and (-1,0) and from there I can find the equations of the lines. Thank you so much!

Re: Need help with tangent lines and derivatives

Quote:

Originally Posted by

**newslang** Hey,

I'm struggling with this one problem from my text book.

"Find the equations of the tangent lines to the parabola y=(x^2)+x that pass through the point (2, -3)."

I know how to find the derivative (2x+1) and then I can find one set of points (5,30) but I can't figure out how to find the other set of points.

Thanks for your help!

Let's say you have a point (p,r) on your parabola. (So, r is given by )

The slope, m, of the line tangent to the parabola when x = p is . (this from your derivative)

The slope, m, of the line passing through points (p, r) and (2, -3) is given by

So that

Plug the in the earlier results for r & m into this. Solve for p. (There will likely be two answers.) You then have the x value(s) for the intersection of the tanget line, with the parabola.

Re: Need help with tangent lines and derivatives