# How do you find the equation of a tangent line to a curve?

Sep 1, 2014

There is no short answer since this is a general question.

You must have a differentiable function to find a tangent line to a curve.

So, let $f \left(x\right)$ be the function for the curve.
And let $f ' \left(x\right)$ be the derivative of $f \left(x\right)$.
Finally, let $x = a$ be the value at which we want the tangent line:

$T \left(x\right) = f \left(a\right) + f ' \left(a\right) \left(x - a\right)$

Note that this is also the formula for linear approximation functions.

There are many examples of tangent line and linear approximation problems, so just search for them.