Question

Given the function f(x)=x2+3x-2

Answer 1

Answer:

  11

Step-by-step explanation:

The average rate of change of function f on interval [a, b] is ...

  m = (f(b) -f(a))/(b -a)

Here, that is ...

  m = (f(6) -f(2))/(6 -2)

So, we need to evaluate the function at x=6 and x=2. Writing it in "Horner form" makes this easier.

  f(x) = (x +3)x -2

  f(6) = (6 +3)6 -2 = 54 -2 = 52

  f(2) = (2 +3)2 -2 = 10 -2 = 8

Then the slope is ...

  m = (52 -8)/4 = 13 -2 = 11

The average rate of change of f(x) from 2 to 6 is 11.