Determine the value(s) of k such that y=-5k is the equation of the tangent line on the graph of F(x) = -x^2 + 4kx + 1
The Attempt at a Solution
not sure where to start this problem; but i understand some fundamentals here. I believe that the tangent will intersect the curve at one point only so I believe that you can equate the two to attempt to solve for k?
1. My derivative of the function ended out to be f'(x) = -2(x -2k)
2. I tried implementing this in to the original function but I ended up with 4k^2 +1 ( then k = 1/2? )
1. After equating the two equations i get -5k = -x^2 + 4kx + 1
2. 0 = -x² + 2.5x + 1 -> x = -0.5 and/or -2
3. I noticed k and x are the same from these two attempts?
What do i do from here? Is everything I've done absolutely garbage or am i on to the correct train of thought?