How do you find the average rate of change of y = 9x^3 - 2x2 + 6y=9x3−2x2+6 over interval [-4,2]?
1 Answer
Jul 10, 2018
Explanation:
"the average rate of change of y over a closed interval"the average rate of change of y over a closed interval
[a,b]" is a measure of the slope of the secant connecting"[a,b] is a measure of the slope of the secant connecting
"the 2 points and is calculated using"the 2 points and is calculated using
(f(b)-f(a))/(b-a)f(b)−f(a)b−a
"here "[a,b]=[-4,2]here [a,b]=[−4,2]
f(b)=f(2)=9(2)^3-2(2)^2+6f(b)=f(2)=9(2)3−2(2)2+6
color(white)(xxxxxxxx)=72-8+6=70××××=72−8+6=70
f(a)=f(-4)=9(-4)^3-2(-4)^2+6f(a)=f(−4)=9(−4)3−2(−4)2+6
color(white)(xxxxxxxxxx)=-576-32+6=-602×××××=−576−32+6=−602
"average rate of change "=(70-(-602))/(2-(-4))average rate of change =70−(−602)2−(−4)
color(white)(xxxxxxxxxxxxxxxx)=672/6=112××××××××=6726=112
