g(x)=7/x, Express the slope of the secant line in terms of x and h.

Question

This problem comes from Sullivan college algebra chapter 3.

Answer 1

Consider an interval between the points x and x+h along the x axis.  The secant line is the line connecting the end points g(x) and g(x+h) on the interval.  The slope of the secant line is the change in y (g(x)) over the change in x for any two points on the line.  The two points are (x,g(x)) and ((x+h),g(x+h))

 

g(x) = 7/x

 

g(x+h) = 7/(x+h)

 

The change in y = g(x+h) - g(x) = 7/(x+h) - 7/x = (7x - 7x - 7h)/x(x+h) = -7h/x(x+h)

 

The change in x = (x+h) - x = h

 

The slope of the secant line then is = change in y/change in x = -7/x(x+h)