How do you find the average rate of change of #y=2x^2-2x+1# over [-1,-1/2]?
1 Answer
Sep 16, 2016
Explanation:
The
#color(blue)"average rate of change"# of y over an interval between 2 points (a ,f(a)) and (b,f(b)) is the slope of the#color(blue)"secant line"# connecting the 2 points.To calculate the average rate of change between the 2 points use.
#color(red)(bar(ul(|color(white)(a/a)color(black)((f(b)-f(a))/(b-a))color(white)(a/a)|)))#
#f(b)=f(-1/2)=2(-1/2)^2-2(-1/2)+1=2 1/2#
#f(a)=f(-1)=2(-1)^2-2(-1)+1=5# The average rate of change between
#(-1,5)" and " (-1/2,2 1/2)# is
#(2 1/2-5)/(-1/2-(-1))=(-2 1/2)/(1/2)=-5# This means that the average of all the slopes of lines tangent to the graph of y between
#(-1,5)"and " (-1/2,2 1/2)# is - 5