Question 124673
To find the average rate of change for a function between two given points, you compute the slope of the secant line, that is the line that passes through the two points.


For your function, {{{f(x)=y=x^2}}}, the value of the function at {{{x=0}}} is {{{f(0)=0^2=0}}}.  So your first point is (0,0)


The value of the function at {{{x=3}}} is {{{f(3)=3^2=9}}}, so your second point is (3,9)


The slope of the line is given by {{{DELTA*y/(DELTA*x)=(y[2]-y[1])/(x[2]-x[1])}}}


{{{(9-0)/(3-0)=3}}}


Therefore your average rate of change is 3.


The green line is the secant line and the red curve is the original function.
{{{graph(200,400,-2,5,-2,10,x^2,3x)}}}