Q. Explain in detail where the formula for the difference quotient comes.
A. The difference quotient is related to the slope formula y2-y1/x2-x1. This means the difference quotient is a fancy way to find the slope of a graph. Also the problem that they give us to use the difference quotient, is just a formula of y=mx+b. we substitute the y-axis with the formula of f(x). This will give us f(x^2)-f(x)/x2-x1. The h is the horizontal direction you will have to go in order to get to the other point.
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