Tangent approximation

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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.

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