How do you find the average rate of change for the function #f(x) = 3x - 2# on the indicated intervals [2,3]?

2 Answers
Alan P.
Aug 1, 2015

The average rate of change for #f(x)=3x-2# on the interval #[2,3]# is #3#

Explanation:

#f(x)=3x-2# is a linear function
#color(white)("XXXX")#with a slope (also called a "rate of change") of 3
#color(white)("XXXX")#for all point on the function line.

Since the rate of change for all points on the line is #3#
the average rate of change for any interval is also #3#

Stefan V.
Aug 1, 2015

#(Deltaf)/(Deltax) = 3#

Explanation:

The average rate of change for a function #f(x)# between two points #x_1# and #x_2# is equal to

#color(blue)((Deltaf)/(Deltax) = (f(x_2) - f(x_1))/(x_2-x_1))#

In your case, you have

#f(x) = 3x-2# and #{(x_1 = 2), (x_2=3) :}#

Use the two values given to you to determine the values of #f(x)# in #x_1# and #x_2#

#f(x_1) = f(2) = 3 * 2 - 2 = 4#

#f(x_2) = f(3) = 3 * 3 - 2 = 7#

The average rate of change for your function between points #2# and #3# will thus be

#(Deltaf)/(Deltax) = (f(3) - f(2))/(3-2)#

#(Deltaf)/(Deltax) = (7 - 4)/1 = color(green)(3)#

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