Question

Find the average rate of change of f(x) = x ^ 2 - 4x + 1 from x = 1 to x = 5 . Simplify your answer as much as possible .

Answer 1

Remember that

The average rate of change is given by the formula

$\frac{f(b)-f(a)}{b-a}$

In this problem we have

b=5

a=1

f(a)=f(1)=(1)^2-4(1)+1=-2

f(b)=f(5)=(5)^2-4(5)+1=6

substitute given values in the formula

$\frac{6-(-2)}{5-1}=\frac{8}{4}=2$

The answer is 2