'What is the average rate of change for the function over the interval, f ( x ) = -x^2+5x between x = 0 and x = 9 ?

2 Answers
Jim G.
May 4, 2018

#-4#

Explanation:

#"the average rate of change of "f(x)" over the interval"#
#"is a measure of the slope of the secant line joining the"#
#"points"#

#"average rate of change "=(f(b)-f(a))/(b-a)#

#"where "[a,b]" is the closed interval"#

#"here "[a,b]=[0,9]#

#f(b)=f(9)=-9^2+(5xx9)=-81+45=-36#

#f(a)=f(0)=0#

#rArr(-36-0)/(9-0)=-4#

Narad T.
May 4, 2018

The average rate of change is #=-4#

Explanation:

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

#=" (f(b) - f(a)) "/" ( b - a )"#

#f(x)=-x^2+5x#

#a=0#

#b=9#

#f(9)=-(9)^2+5xx9=-81+45=-36#

#f(0)=-0+0=0#

The average rate of change is

#=(-36-0)/(9-0)=-36/9=-4#

Related questions
Impact of this question
6015 views around the world
You can reuse this answer
Creative Commons License