How do you find the average rate of change for the function #f(x) = 2 / (x+1)# on the indicated intervals [0,h]?

1 Answer
Alan P. · George C.
Oct 9, 2015

Average rate of change #= -2/(h+1)#

Explanation:

The average rate of change for a continuous function #f(x)# over an interval is
#color(white)("XXX")("the change in "f(x)" between the endpoints")/("width of the interval")#

In this case:
#color(white)("XXX")(color(red)(f(h))-color(blue)(f(0)))/color(green)((h-0))#

#color(white)("XXX")(color(red)((2/(h+1))) - color(blue)(2/(0+1)))/color(green)(h)#

#color(white)("XXX")(color(red)(2/(h+1))-color(blue)((2h+2)/(h+1)))/color(green)(h)#

#color(white)("XXX")=((-2h)/(h+1))/color(green)(h)#

#color(white)("XXX")=-2/(h+1)#

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