How do you find the average rate of change for the function #f(x)=x^(+2)# on the indicated intervals [4,6]?

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How do you find the average rate of change for the function #f(x)=x^(+2)# on the indicated intervals [4,6]?

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Answer 1 · 2015-08-21T14:55:28

The average rate of change of a function #f# on an interval #[a,b]# is #(f(b) - f(a))/(b-a)#

Explanation:

For #f(x)=x^2# on the interval [4,6],

The average rate of change is:

#(f(6) - f(4))/(6-4) = ((6)^2-(4)^2)/2 = 20/2 = 10#

Note that the average rate of change is also the slope of the line through the point on the graph of #f# where #x=4# and where #x=6#. That is, through the points: #(4,16)# and #(6, 36)#

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How do you find the average rate of change for the function #f(x)=x^(+2)# on the indicated intervals [4,6]?

1 Answer

Explanation:

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