- The difference quotient allows us to see the slope from the tangent line. This also known as the derivative in calculus. On the picture shown above we are able to see that the tangent line only touches the graph once and is known to be (x). But the image does not only show the line touching one point, but two points. When the line touches two points we are able to identify it to be a secant line.
- Since we have two points, now we focus on finding the slope, which is y1-y2/ x1-x2 . As shown in the image the ywo given points are (x1,Y1) and (x1+h, y2), and between these two given points there is a change in h, also known as delta h. This leads us to the form of ( x, f(x1)) and (x+h, f(x+h)). (if any confusion: Picture is different , instead of y2 it should be replaced in of f(x). And by using the slope formula we plug in the points, and solve it a slope formula problem. Thats how we get the difference quotient, this mainly only focuses on secant line. To find the secant line we could just plug in the lim. of zero into the difference quotient and find secant line.
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