I need help with this math

Question

Use the function below to find the average rate of change for the given interval. 

f(x)=6x^2-8x+5

2<x<4

Answer 1

f(x) = 6x^2 -8x +5

average rate of change from x=2 to x= 4

find the two points (x,y) = (2, f(2)) = (2,24-16+5) and (4, f(4))= (4,96-32+5)

= (2, 13) and (4, 69)

then find the slope of the line connecting them

= (69-13)/(4-2) = 56/2 = 28 = average rate of change

or find f'(x) = 12x -8

then find f'(2) = 16

and f'(4) = 48-8 =40

average of 16 and 40 = 56/2 = 28 = average rate of change