Final answer:
The instantaneous rate of change of the function f(x) = 4x^2 - 3x at x = -1 is found by calculating the derivative f'(x) = 8x - 3 and evaluating it at x = -1, which gives -11.
Step-by-step explanation:
The student is asking to find the instantaneous rate of change of the function f(x) = 4x^2 - 3x at x = -1. To do this, we first need to find the derivative of the function, which represents the rate of change of the function with respect to x.
To find the derivative of the function f(x), we apply the power rule. This gives us:
- The derivative of 4x^2 is 8x.
- The derivative of -3x is -3.
So the derivative of f(x), or f'(x), is 8x - 3. To find the instantaneous rate of change at x = -1, we simply substitute -1 into the derivative function:
f'(-1) = 8(-1) - 3 = -8 - 3 = -11.
Therefore, the instantaneous rate of change of the function f(x) = 4x^2 - 3x at x = -1 is -11.