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{y²-y¹}{x²-x¹}\ </math>

Utilizing cross-multiplication, this yields:

<math> y²-y¹ = \frac{dy}{dx}\ x²-x¹</math>

When one point on the curve is known, its x and y values are plugged into the equation.