Final answer:
The second derivative of a function f(x) is denoted as f''(x). It measures how the rate of change of the function's value is changing, giving us information on the concavity or acceleration of the function. The correct representation of the second derivative is option a. f''(x).
Step-by-step explanation:
The question posed is about determining which option correctly represents the second derivative of a function f(x). The function f(x) is simply the original function, and its first derivative f'(x) represents the rate at which the function's value is changing at any point. The second derivative, denoted as f''(x), measures how the rate of change itself is changing, which means it gives us information about the concavity and/or the acceleration of the function.
Given the list of options:
• a. f''(x)
• b. f'(x)
• c. f(x)²
• d. 2f(x)
The second derivative of y = f(x) is correctly represented by option a. f''(x). This is because f''(x) is the notation for the derivative of the first derivative of the function, thus being the second derivative.