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:

${\frac {dy}{dx}}\ ={\frac {rise}{run}}\ ={\frac {y-y'}{x-x'}}\$

Utilizing cross-multiplication, this yields:

$y-y'={\frac {dy}{dx}}\ x-x'$

When ( x' , y' ) is a known point on the line.