Tangent approximation

The tangent approximation method is a method in Calculus employed to find the equation of a line tangent to the curve. One must know the slope of the curve and a point on the curve. The slope is usually found by taking the derivative of the equation and equating it to the change in y over the change in x:

<math> \frac{dy}{dx}\ = \frac{rise}{run}\ = \frac{y - y'}{x - x'}\ </math>

Utilizing cross-multiplication, this yields:

<math> y - y' = \frac{dy}{dx}\ x - x'</math>

When <math> ( x' , y' ) </math> is a known point on the line.