Let g(x)=4x^2-2. what is the average rate of change from -2 to 4.

Question

Let g(x)=4x^2-2. what is the average rate of change from -2 to 4 ?

Answer 1

g(x) =4*x² - 2

 

g(x) evaluated at x= -2 is 4*(-2)² - 2 = 14

 

g(x) evaluated at x = 4 = 4*(4)² - 2 = 62

 

The average rate of change is the slope of the secant line joining the points (in this case) (-2, 14) and (4, 62).

 

The slope of the secant line is (62 - 14)/[4 -(-2)] = 48/6 = 8

 

Going back, then, to the original question, the average rate of change of g(x) from x=(-2) to x=4 is 8.