How do you find the average rate of change of #f(x) = 3/(x-2)# over the interval [4,7]?

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Answer 1 · 2017-08-05T00:47:17

Please see below.

Memorize this:

The average rate of change of a function #f# over an interval #{a,b]# is

#(f(b)-f(a))/(b-a)#.

For this question, we have #f(x) = 3/(x-2)# and #[a,b] = [4,7]#

So the average rate of change is

#(f(7)-f(4))/(7-4) = (3/(7-2) - 3/(4-2))/(3)#

# = (3/5-3/2)/3 = ((3*2)/(5*2) - (3*5)/(2*5))/3#

# = ((6-15)/10)/(3/1) = ((-9)/10)/(3/1)#

# = (-9)/10 * 1/3 = -3/10#