BQ 7: Unit V

The formula for the difference quotient is f(x+h)- f(x) divided by h. It is derived from the slope formula of y^2-y^1/x^2-X^1. The only difference is that as seen on the graph the section of x+h is substituted  in the place of y^2 and then y with x. Next its done the same with the bottom leaving it as x+h-x. Next you move on by canceling out the x's leaving the h on the bottom. So its simply substituting in the correct values into the slope formula resulting in the difference quotient. This all being shown in the image provided. The image shows how delta x can be used as another notation for the h. The purpose always being to get delta x as small as possible, making the tangent line less steep. Because the smaller the delta x, the more the secant and tangent lines resemble one another.