What is the slope of a horizontal tangent line?

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What is the slope of a horizontal tangent line?

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Answer 1 · 2014-07-23T18:21:42

The slope of a horizontal tangent line is 0.

To calculate the slope of a straight line, we take a difference in the $y$ $y$ dimension and divide it by the change in the $x$ $x$ dimension of two points on the line:

$slope = \frac{y_{1} - y_{2}}{x_{1} - x_{2}}$ $"slope" = (y_1 - y_2)/(x_1 - x_2)$ assuming points $(x_{1}, y_{1})$ $(x_1, y_1)$ and $(x_{2}, y_{2})$ $(x_2, y_2)$ lie on the line

For a horizontal line $y_{1} - y_{2} = 0$ $y_1 - y_2 = 0$ so

$slope = \frac{0}{x_{1} - x_{2}} = 0$ $"slope" = 0/(x_1 - x_2) = 0$

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What is the slope of a horizontal tangent line?

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