From the course: Complete Guide to Calculus Foundations for Data Science
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Tangent lines and slopes
From the course: Complete Guide to Calculus Foundations for Data Science
Tangent lines and slopes
- [Instructor] Next, let's take a moment to understand derivatives as the slope of a tangent line. Before I explain this concept, though, let's take a moment to understand secant lines. A secant line is a line that intersects at least two distinct points of another line. You can use the slope of a secant line at a point a, f of a to estimate the rate of change where the output changes in relation to the input. You can obtain the slope of a secant line at points x, f of x and a, f of a with the equation f of x minus f of a, divided by x minus a. You can replace x in this equation with the values a plus h, where h is a value close to 0. This gets you the equation f of a plus h, minus f of a, divided by a plus h minus a. You can simplify the denominator to f of a plus h, minus f of a, divided by h. This should look familiar to your derivative definition that you saw earlier. In this graph, you can see a secant line, so you have the parabola that looks like a U with the blue line, and…
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