How do you find the average rate of change of #y=x^2+6x+10# over [1,3]?

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Answer 1 · 2016-12-08T07:58:55

#(Delta y)/(Delta x) = 10#

Given:

#f(x) = x^2+6x+10#

The average rate of change of #f(x)# over any interval #[a, b]# is:

#(Delta f(x))/(Delta x) = (f(b)-f(a))/(b-a)#

In other words, it is the slope of the chord joining #(a, f(a))# and #(b, f(b))#

In our example, we find:

#f(1) = 1^2+6(1)+10 = 17#

#f(3) = 3^2+6(3)+10 = 37#

So the average rate of change of #f(x)# over #[1, 3]# is:

#(Delta f(x))/(Delta x) = (f(3)-f(1))/(3-1) = (37-17)/2 = 20/2 = 10#