Difference between revisions of "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'': | 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< | + | <math> \frac{dy}{dx}\ = \frac{rise}{run}\ = \frac{y<sup>2</sup>-y<sup>1</sup>}{x<sup>2</sup>-x<sup>1</sup>}\ </math> |
Utilizing cross-multiplication, this yields: | Utilizing cross-multiplication, this yields: | ||
| − | <math> y< | + | <math> y<sup>2</sup>-y<sup>1</sup> = \frac{dy}{dx}\ x<sup>2</sup>-x<sup>1</sup></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. | ||
Revision as of 13:28, April 5, 2008
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{y2-y1}{x2-x1}\ </math>
Utilizing cross-multiplication, this yields:
<math> y2-y1 = \frac{dy}{dx}\ x2-x1</math>
When one point on the curve is known, its x and y values are plugged into the equation.