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 - y'}{x - x'}\ </math> | <math> \frac{dy}{dx}\ = \frac{rise}{run}\ = \frac{y - y'}{x - x'}\ </math> | ||
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When ( ''x' '', ''y' '') is a known point on the line. | When ( ''x' '', ''y' '') is a known point on the line. | ||
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| + | [[Category:Calculus]] | ||
Latest revision as of 01:09, August 31, 2011
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 - y'}{x - x'}\ </math>
Utilizing cross-multiplication, this yields:
<math> y - y' = \frac{dy}{dx}\ x - x'</math>
When ( x' , y' ) is a known point on the line.