I was given the function $f(x)=k\sqrt{x}$, and a line $y=x+4$. I need to find a value for k such that the line is tangent to the graph. I have attempted the problem by taking the derivative of the given function.
Derivative
$$f'(x)=\frac{k}{2\sqrt{x}}$$
Since the slope of the tangent line is $1$, I set the derivative equal to $1$ and get:
$$1=\frac{k}{2\sqrt{x}}$$ and then I get: $$2\sqrt{x}=k$$
I feel like I am on the right track, but I am clueless on how to find an x to ensure I find the right k. What other process would be necessary to find k, assuming I am on the right track?