Finding the rate of change in a function?

Question

Find the average rate of change of the function from x1 to x2?
Function: f(x) : x^2 - 3x + 7
x values: x1 = 1, x2 = 6

Answer 1

The function f(x) = x² - 3x + 7

Average rate of change = [f(x₂) - f(x₁)]/(x₂ - x₁)

x₁ = 1, x₂ = 6

f(x₁)

f(1) = (1)² - 3(1) + 7

 = 1 - 3 + 7

 = 5

f(x₂)

f(6) = (6)² - 3(6) + 7

= 36 - 18 + 7

= 25

Average rate of change = ( 25 - 5)/(6 - 1)

= 20/5

Average rate of change = 4.