Consider the graph of g(x) shown below. (a) If g(x) is the first derivative of f(x), what is the nature of f(x) when x = 1? (b) If g(x) is the second derivative of f(x), what is the nature of f(x) when x = 3? Ay (a) If g(x) is the first derivative of f(x), what is the nature of f(x) when x = 1? O A. f(x) is decreasing at x = 1. O B. f(x) is increasing at x = 1. O C. f(x) has a local minimum at x = 1. O D. f(x) has a local maximum at x = 1. (b) If g(x) is the second derivative of f(x), what is the nature of f(x) when x = 3? O A. f(x) has an inflection point at x = 3. O B. f(x) is concave up at x = 3. O C. f(x) is concave down at x = 3