How do you find the average rate of change for the function #y=X^2 + 5X# on the indicated intervals [2,5]?

2 Answers
Aug 28, 2015

The average rate of change is 2

Explanation:

In general the rate of change of #y=x^2+5x# is
#color(white)("XXXX")(dy)/(dx)=2x+5#

At #x=5#
#color(white)("XXXX")(dy)/(dx) = 2(5)+5 = 15#

At #x=2#
#color(white)("XXXX")(dy)/(dx)=2(2)+5=9#

Between #x=2# and #x=5#
#color(white)("XXXX")(dy)/(dx)# changes by # 15-9=6#

The distance between (#x=2#) and (#x=5#) is #5-2 = 3#

The average rate of change (per unit change in #x#) is
#color(white)("XXXX")6/3 =2#

Aug 28, 2015

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

Explanation:

The average rate of change of a function #f(x) = x^2+fx# on an interval #[2,5]# is:

#(Deltaf)/(Deltax) = (f(5)-f(2))/((5)-(2))#

# = (50 - 14)/(3) = 36/3 = 12#