Final answer:
To find f"(2), we differentiate the given functional equation using the chain rule and product rule, then evaluate the resulting expressions using the known values of f(4), f'(4), and f"(4).
Step-by-step explanation:
The question asks to find the second derivative of the function f at the point x=2, given a functional equation f(x)= (x²-1)f(2x) and values for f(4), f'(4), and f"(4). To solve this, we can differentiate the given functional equation with respect to x, and then evaluate the resulting expressions for the derivatives at the appropriate points. The chain rule and product rule from calculus are key to finding the necessary derivatives. Applying these rules in a step-by-step manner allows us to express f"(2) in terms of the given information about the function at x=4.