Question

what does f'(3) mean? is it on the x- axis?

Answer 1

f'(3) is the slope of the tangent line at x=3

Answer 2

no
\[f'(3)\] is a number. it is the derivative evaluated at the number 3.
3 is on the x-axis,
\[f'(3)\] would be on the y - axis if you were graphing
\[y=f'(x)\]

Answer 3

and this tangent line touches the graph of f(x) at x=3