Final answer:
The graph of the function f(x) = 17x² + 3 is concave upward on the interval (-∞, ∞) as the second derivative f''(x) = 34 is always positive and there are no intervals where the graph is concave downward.
Step-by-step explanation:
The question asks to determine the open intervals on which the graph of f(x) = 17x² + 3 is concave upward or concave downward.
To determine concavity, we need to examine the second derivative of the function.
The second derivative of f(x) is f''(x) = 34, which is a constant and is always positive.
Since the second derivative is always positive, the graph of f(x) is concave upward on the entire real number line.
Therefore, the graph is concave upward on the interval (-∞, ∞).
Since the second derivative does not change sign, there are no intervals on which the graph is concave downward.
The answer would be 'DE' (Does not exist) for concave downward intervals.