Hi! I am doing some problems to practice for a math competition, and I'm wondering if I did this correctly. I don't really have an answer sheet, so I have no way of knowing whether I'm right. If you would please review it, that would be cool!
There are exactly two values of m for which the line y=mx-12 is tangent to the parabola y=x^2-3x+5. Determine those two values.
The Attempt at a Solution
Okay so first I found the derivative of y=x^2-3x+5.
This is the slope, so I put it into the equation of the tangent line:
y=mx-12=(2x-3)x-12=2x^2-3x-12 <-- the tangent line
Now I made the the two equations equal to each other because they intersect at one point, right?
and when I solve for x it gives me +/- √17
I put this into the equation for the slope and I get:
m= 2√17 -3 or m=-2√17 -3
Is this correct? Thank you in advance.