Question

Suppose f(x)=x^2+6x+2 
What is the average rate of change of f(x) with respect to x as x changes from -1 to 1?

 

Answer 1

Given function f(x) = x^2+6x+2

a = -1, b = 1

f(-1) = (-1)^2+6(-1)+2

 = 1-6+2

= -3

f(1) = (1)^2+6(1)+2

= 1+6+2

= 9

Average rate ofchange = (f(b)-f(a))/(b-a)

= [9-(-3)]/(1-(-1))

= (9+3)/(1+1)

= 12/2

= 6