Question: Average rate of change. Instantaneous rate of change (1st derivative).

Suppose that the function f(x) = (X^3/27) + 10 is used to simulate the performance of one

investment, in thousands of CHF, x years after January 1, 2000. Evaluate the following situations:

(a) The average rate of change of the investment between the dates January 1, 2003 and

January 1, 2006.

(b) The average rate of change of the investment between the dates January 1, 2006 and

January 1, 2009.

(c) The instantaneous rate of change of f(x) at any time x.

(d) The instantaneous rate of change of f(x) at year x = 6.