Mathematical notation for 'The tangent of $f(x)$ at the point $(x,y)$

Question

I've been looking around and can't seem to find correct mathematical notation for the tangent of a function at some point $(x,y)$.

For example, if a question asks to find the equation of the tangent of $f(x) = x^2$ at the point $(2,4)$, i'd solve it this way:

$$f'(x) = 2x$$ $$f'(2) = 4$$

So, let the tangent be denoted by the linear function $g(x)$

$$g(x) = 4x + c$$ $$g(2) = 4$$ $$g(x) = 4x - 4$$

Is there a mathematical symbol representing the tangent in this situation? Is what i've written the 'common practice'?

Answer 1

I'm not aware of any symbol for the tangent line, but using the notation $g(x)=\dots$ looks fine to me, as long as you explicitly state that the function $g$ describes a tangent line. In general, the tangent to the graph of $f$ at the point $\left(a,f(a)\right)$ is given by $$ g(x)=f'(a)(x-a)+f(a) \, . $$ In this context, is simpler to use the point-slope equation of a straight line.