Find the equations of the 2 tangent lines to the graph of f that pass through the indicated point.
f(x)= 4x-x^2 point is (2, 5)
The farthest I have gotten with this is writting this:
(a^2-5)/(a-2)
The next thing is I'm trying to figure out the equal thingy..
a^2-5 = ???
I think I see what may need to be done...
Let be a point on the function.
Then,
Thus, the tangent line has the form
So we see that
This line passes through the point , so our equation becomes:
So we get
Getting all the terms on side, we see that
So
Thus, and
Therefore, we get two different tangent lines:
Does this make sense?
The graph verifies this:
--Chris
Yup, those 2 are the answers..
The stupid thing is though, I just had to take the slope from (2,5) and the other 2 points on the graph, and I would've gotten the answer..
The question would've only taken me a minute, and it ends up taking 20 minutes trying to find stuff, lol.