Find the average rate of change of the function f(x)=x^2+4x from x1=1 to x2=-7

Answer 1

as always, the average rate of change over an interval [a,b] is just the slope of the line joining the two points on the graph:

∆y/∆x = (f(b)-f(a))/(b-a)
so, for this one, that is
(f(1)-f(-7))/(1 - (-7)) = (5-21)/(8) = -2

Answer 2

f(x)=x2-1