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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'':
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{y<sub>2</sub>-y<sub>1</sub>}{x<sub>2</sub>-x<sub>1</sub>}\</math>
<math> \frac{dy}{dx}\ = \frac{rise}{run}\ = \frac{y<sub>2</sub>-y<sub>1</sub>}{x<sub>2</sub>-x<sub>1</sub>}\</math>
Utilizing cross-multiplication, this yields:
Utilizing cross-multiplication, this yields:
<math> y<sub>2</sub>-y<sub>1</sub>=\frac{dy}{dx}\ x<sub>2</sub>-x<sub>1</sub></math>
<math> y<sub>2</sub>-y<sub>1</sub> = \frac{dy}{dx}\ x<sub>2</sub>-x<sub>1</sub></math>
When one point on the curve is known, its x and y values are plugged into the equation.
When one point on the curve is known, its x and y values are plugged into the equation.