Final answer:
The instantaneous rate of change of f(x) = 3x² - 7x + 12 when x = 5 is 23.
Step-by-step explanation:
To find the instantaneous rate of change of f(x) = 3x² - 7x + 12 when x = 5, we need to calculate the derivative of f(x) and then substitute x = 5 into the derivative.
The derivative of f(x) is given by f'(x) = 6x - 7. Substitute x = 5 into the derivative: f'(5) = 6(5) - 7 = 23.
Therefore, the instantaneous rate of change of f(x) when x = 5 is 23.