Final answer:
The instantaneous rate of change of the function f(x) = 3x^2 + 2x - 1 at x = -1 is -4, which is obtained by evaluating the derivative of the function, f'(x) = 6x + 2, at that point.
Step-by-step explanation:
The question is asking us to find the instantaneous rate of change of the function f(x) = 3x2 + 2x - 1 at x = -1. The instantaneous rate of change can be found by taking the derivative of the function and evaluating it at the given point.
First, let's find the derivative of f(x) which is f'(x). Using the power rule, the derivative of xn is nxn-1, so:
f'(x) = 2 * 3x1 + 2 * 1 - 0
f'(x) = 6x + 2
Now, we evaluate the derivative at x = -1:
f'(-1) = 6(-1) + 2 = -6 + 2 = -4
Therefore, the instantaneous rate of change of f(x) at x = -1 is -4.