# How do you find the average rate of change of #y = 9x^3 - 2x2 + 6# over interval [-4,2]?

##### 1 Answer

Jul 10, 2018

#### Explanation:

#"the average rate of change of y over a closed interval"#

#[a,b]" is a measure of the slope of the secant connecting"#

#"the 2 points and is calculated using"#

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

#"here "[a,b]=[-4,2]#

#f(b)=f(2)=9(2)^3-2(2)^2+6#

#color(white)(xxxxxxxx)=72-8+6=70#

#f(a)=f(-4)=9(-4)^3-2(-4)^2+6#

#color(white)(xxxxxxxxxx)=-576-32+6=-602#

#"average rate of change "=(70-(-602))/(2-(-4))#

#color(white)(xxxxxxxxxxxxxxxx)=672/6=112#