Here's the problem:

"Find the x-coordinate of all points on the graph of

where the tangent line is parallel to the line

."

I took the derivative of f(x) and got

. Then I set the slope of the line y equal to this equation, so as to have

. So I solved for x and got

and so x=1.225 (after taking the square root).

I went ahead and found the actual tangent line of this by plugging that x-value back into the derivative of f(x), ending with

.

I'm pretty sure I did the process right, but if I didn't, could someone kindly correct me? Or tell me if I'm leaving something out? I feel like there's something else that should be done.