How do you find the average rate of change of # f(x)=x^2-2x# from 1 to 5?

1 Answer
Mia
Nov 17, 2016

The average rate is #4#.

Explanation:

The average rate of a function #" " f(x)" "#between
#" "#
#a" " and" "b" "#is defined as:
#" "#
#" "#
#(f(b)-f(a))/(b-a)#
#" "#
#" "#
The average rate of the function #f(x) # between #" "5" " and " "1#
#" "#
#(f(5)-f(1))/(5-1)#
#" "#
#" "#
Let us evaluate #" "f(5)" and" " f(1)" "#
#" "#
#f(5) = 5^2 -2(5) = 25 - 10=15#
#" "#
#f(1) = 1^2 - 2(1) = 1-2 = -1#
#" "#
#(f(5)-f(1))/(5-1)=(15-(-1))/(5-1)=(15+1)/4 = 16/4 =4#
#" "#
Hence ,
#" "#
The average rate is #4#.

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