Rate of Change

Question

Find the average rate of of change of f(x) = -2x^2 +6

a. from 2 to 4

b. from -1 to 1

c. from -3 to o

Answer 1

The average rate of change would be the slope of the line through each of the endpoints of the function values over the interval.

                                                    y₂-y₁

                                             m = -------

                                                    x₂-x₁

     x₁ y₁  x₂  y₂

a. (2,-2), (4,-26)    -26-(-2) / 4-2  = -24/2 = -12         y_{1 = -2(2)² + 6 = -2*4 + 6 = -8 + 6 = -2,  so (2,-2)}

                                                           m = -12

b. same method as in part a

 

c. same method as in part a

Answer 2

Rate of change = (f(b) - f(a))/(b-a)

 

1. (-26 - -2)/(4-2) = -24/2 = -12

2. (4 - 4)/(1- -1) = 0/2 = 0

3. (6 - -12)/(0 - -3) = 18/3 = 6