# What is the purpose of a derivative?

A derivative is a slope function: $m = f ' \left(x = v a l u e\right)$. If you want to find the slope anywhere along the function, you can.
If you want to find a tangent line at a specific point along the function you can, using the slope and the point: $y - {y}_{1} = m \left(x - {x}_{1}\right)$