Find the equations for the two tangent lines.

[Jinxypo]

Homework Statement

Find the equations for the two tangent line on the graph f(x) = - (x-3)^2 - 4 through the point (2,5)

Homework Equations

The Attempt at a Solution

I already solved for f '(x) which is -2x +6. Then I plug in 2 for f '(x) in order to find the slope, which is 2. Using the equation y - y1 = m(x -x1) I found the equation for my first tangent line to be y = 2x+1. My question is how do i find the second tangent line, and did I do something wrong?

 

[fzero]

The point (2,5) is not on the curve y = f(x). Furthermore, the tangent line to f(x) at x=2 does not pass through the point (2,5). y=f(x) is a parabola, you need to consider the lines from points (x,f(x)) on the curve that pass through (2,5) and then solve for the lines whose slope matches f'(x).