Instantaneous rate of exchange for f(x) = x - x^3 where x is -1

Answer 1

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.

Therefore, the instantaneous rate of exchange for f(x) = x - x^3 at x = -1 is -2.