How do you find the average rate of change of #k(x)=x/(x^2+1)# over [1,2]?

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Answer 1 · 2016-09-15T09:01:48

#-3/10#.

The average rate of change of y = k(x) over an interval #x in [a, b] is

#(intk'dx)/(intdx)#, over #x in [a, b]#

#(k(b)-k(a))/(b-a)#, using #k'dx=(dk)/(dx)dx=dk# and int dk = k,

between the limits.

Here, it is

#(2/(2^2+1)-1/(1^2+1))/(2-1)#

#=-3/10#.