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 (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 \frac{dy}{dx}\=\frac{rise}{run}\=\frac{y₂-y₁}{x₂-x₁}\}

Utilizing cross-multiplication, this yields:

$y₂-y₁={\frac {dy}{dx}}\ x₂-x₁$

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