Question

What is the average rate of change of f(x)=2x^2+4x-3 between x=1 and x=6

Answer 1

The ave. r. of c. of a function f(x) on the interval [a,b] is given by:

             f(b) - f(a)
a.r.c. = --------------
               b - a

Here f(x) = 2x^2 + 4x - 3, a = 1 and b = 6.  Therefore,

f(a) = f(1) = 2(1)^2 + 4(1) - 3 = 3, and f(b) = f(6) = 2(6)^2 + 4(6) - 3 = 93

So the a. r. c. is then

              93 - 3         90
a.r.c. = ---------- = --------- = 18 (answer)
               6-1             5