Final answer:
The function g(x) = 1/x² is concave down for all x values.
Step-by-step explanation:
To determine the interval for which the function g(x) = 1/x² is concave down, we need to find where the second derivative of the function is negative. Let's first find the second derivative of g(x).
Let's start with the function g(x) = 1/x². Taking the derivative of g(x), we get g'(x) = -2/x³. Taking the derivative of g'(x), we get g''(x) = 6/x⁴. Now, we need to find where g''(x) is negative.
Since the denominator x⁴ is always positive, g''(x) will be negative when the numerator 6 is negative. Therefore, g(x) = 1/x² is concave down for all x values.