Find the average rate of change of f(x)=2x^2-x+1 on the interval [3, 3+h]

Question

Not sure if the graph is entirely relavant to solving this homework problem. Struggling to understand what to do for A.R.C. with the variable in the interval.

Answer 1

I think the ARC is just [ f(3+h)  -f(3) ] /h 

this works out to   2 h + 11 

 

The rational is that the average value of a function, g,  on an interval [ a, b] is

∫ g(x) dx  / (b -a)   {upper limit = b , lower limit = b}

 

For a rate of change it is the derivative that must be integrated.  But the integral of a derivative is the original function.