diff --git a/packages/smath/examples/Tangent Line.md b/packages/smath/examples/Tangent Line.md index cb46c7b..2b64874 100644 --- a/packages/smath/examples/Tangent Line.md +++ b/packages/smath/examples/Tangent Line.md @@ -2,14 +2,14 @@ The tangent line to a curve is a line that passes through a single local point on the curve, that also matches the same slope. That means, the derivative of the curve must match the slope of the tangent line. -Let's assume our curve is defined by the formula below and we want to find the tangent line at \(x_{0}=1\). +Let's assume our curve is defined by the formula below and we want to find the tangent line at \\\(x_{0}=1\\\). $$f(x) = \frac{1}{8}x^{2} - x - 4$$ -We could plug in \(f(x_{0})\) to obtain \(y_{0}\), then compute the derivative \(f'(x_{0})\) to obtain the slope, and then plug in our values into point-slope form. +We could plug in \\\(f(x_{0})\\\) to obtain \\\(y_{0}\\\), then compute the derivative \\\(f'(x_{0})\\\) to obtain the slope, and then plug in our values into point-slope form. $$y-y_{0}=m(x-x_{0})$$ -Finally, we can rewrite this formula in y-intercept form \(y=mx+b\) where \(b=y_{0}-mx_{0}\). +Finally, we can rewrite this formula in y-intercept form \\\(y=mx+b\\\) where \\\(b=y_{0}-mx_{0}\\\). $$y=mx+(y_{0}-mx_{0})$$ \ No newline at end of file