Calculate the average rate of change for the function f (x) = x4 + 3x3 - 5x2 + 2x - 2, from x = - 1 to x = 1

Average rate of change over the interval [a, b] for y = f (x) is given by f (b) - f (a) b-a

Hence, average rate of change of from x=-2 to x=6 i. e. over the interval [-2,6] for y = f (x) = 12 x2 is given rate of change = f (6) - f (-2) 6 - (-2)

As f (-2) = 12 (-2) 2 = 2 and f (6) = 12 (6) 2 = rate of change = 18-2 8 = 162 = 2