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## Homework Statement

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

## Homework Equations

n/a

## 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?

**Attempt 1:**

1. My derivative of the function ended out to be f'(x) = -2(x -2k)

2. I tried implementing this into the original function but I ended up with 4k^2 +1 ( then k = 1/2? )

**Attempt 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?