The average rate of change of a function over an interval is calculated by finding the slope of the secant line that intersects the graph of the function at the endpoints of the interval.In this case, the function is Y=-16x^2+100x and the interval is [4, 6]. To find the slope of the secant line, we need to find the values of Y at 4 and 6.When x=4, Y=-16(4)^2+100(4)=160When x=6, Y=-16(6)^2+100(6)=240The slope of the secant line is 240-160/6-4=40/2=20Therefore, the average rate of change of Y over the interval [4, 6] is 20.We can also find the average rate of change by using the formula:
Average rate of change = (f(b)-f(a))/(b-a)
In this case, f(a)=Y(4)=160 and f(b)=Y(6)=240. Therefore, the average rate of change is:
Average rate of change = (240-160)/(6-4) = 40/2 = 20