Unit V Big Question

1. When we take a point in the graph we label it (x, f(x)) and when we move the point to the left we get delta x which is another way of saying h. What connects these two points is the secant line, which goes through TWO points. We then have to find the slope where we use the formula y2-y1/x2-x1. We then plug in our (x, f(x)) into it as (x,y) in order to get the slope. This gives us f (x+h)-f(x)/h because the x’s cancel. So we also know that the smaller delta x is the more similar the secant line becomes like tangent. In order for it to work both the secant and tangent line must overlap, since tangent is only ONE point. So to find tangent all we do is take the limit as x approaches 0. We do this because we are trying to get delta x as smallest as possible that it almost reaches 0. This gets the delta x as small as possible which is what we want and where the different quotient comes from.