Question 126975
The average rate of change of f(x) between x = a and x = b is given by the slope of the line that passes through the points (a, f(a)) and (b, f(b)) (called a secant line).  Given two points, you can calculate a slope using the formula:


{{{m=(y[1]-y[2])/(x[1]-x[2])}}}, so for the slope of the described secant line:


{{{(f(a)-f(b))/(a-b)}}}


For your function:


{{{a = -4}}}, so {{{f(a)=f(-4)=(-4)^2-10(-4)=16+40=56}}}


{{{b= 1}}}, so {{{f(b)=f(1)=(1)^2-10(1)=1-10=-9}}}


{{{(f(a)-f(b))/(a-b)=(56-(-9))/(-4-1)=65/-5=-13}}}


Let's draw a picture and see if the answer makes sense:


{{{drawing(600,600,-10,10,-60,60,
grid(1),
graph(600,600,-10,10,-60,60,x^2-10x,-13x+4)
)}}}


The secant line pictured doesn't look as steep as it should be for a -13 slope, but that is because I have different scales for the x and y axis so that you can actually see something.  But the intersection points look correct and the configuration of the parabola is right (vertex at (5,-25), zeros at 0 and 10, concave up, etc.)