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:
Failed to parse (syntax error): {\displaystyle \frac{dy}{dx}\ = \frac{rise}{run}\ = \frac{y<sub>2</sub>-y<sub>1</sub>}{x<sub>2</sub>-x<sub>1</sub>}\}
Utilizing cross-multiplication, this yields:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y<sub>2</sub>-y<sub>1</sub> = \frac{dy}{dx}\ x<sub>2</sub>-x<sub>1</sub>}
When one point on the curve is known, its x and y values are plugged into the equation.