1.To find the difference quotient we have to get a graph. Then though that graph we draw a line that touches the graph at two point and we call that the secant line. The coordinate for point A(the first point) is (x,f(x)) and point B has coordinates of (x+h,f(x+h)). We need to calculate the slope of the secant line by slope formula which is y2-y1/x2-x1. Y2=f(x+h), Y1=f(x), X2=x+h, X1=x. The equation should be f(x+h)-f(x)/x+h-x. The x's at the bottom cancel leaving the slope to be f(x+h)-f(x)/h, which is the difference quotient formula.
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| http://cis.stvincent.edu/carlsond/ma109/diffquot.html |
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| http://simple.wikipedia.org/wiki/Difference_quotient |
