Answer: Therefore, the instantaneous rate of exchange for f(x) = x - x^3 at x = -1 is -2.
Step-by-step explanation: To find the instantaneous rate of exchange for f(x) = x - x^3 at x = -1, we need to find the derivative of the function and then evaluate it at x = -1.
Taking the derivative of f(x) = x - x^3 using the power rule, we get:
f'(x) = 1 - 3x^2.
Now, evaluating f'(x) at x = -1:
f'(-1) = 1 - 3(-1)^2.
Simplifying,
f'(-1) = 1 - 3(1) = 1 - 3 = -2.