Que Find the average rate of change of the function from x1

Que : Find the average rate of change of the function from x₁ to x₂.

f(x) = x² 2x + 9

x₁ = 1, x₂ = 6

Solution

Given that

f(x) = x² - 2x + 9

where x1 = 1 ,x2 = 6

Hence,

f(x1) = f(1) = 1² - 2.1 + 9

= 1 - 2 + 9

= 8

f(x2) = f(6) = 6² - 2.6 + 9

= 36 -12 + 9

= 33

Average rate of change of the function from x1 to x2 = [f(x2) - f(x1) ] / (x2 - x1)

=( 33 - 8 ) / (6 - 1)

= 25 / 5

= 5

Therefore,

Average rate of change of the function from x1 to x2 = 5