Questions: (h) What is the number at which f has a relative minimum (i) What is the relative minimum of f ?

Solution Steps

To find the number at which \( f \) has a relative minimum, we need to determine the critical points of the function \( f \) by finding where its derivative \( f' \) is zero or undefined. Then, we can use the second derivative test or the first derivative test to identify which of these critical points corresponds to a relative minimum.

The function \( f \) is not explicitly defined in the output, as it is represented by an ellipsis. Therefore, we cannot determine the critical points or the relative minimum without knowing the specific form of \( f \).

The first derivative \( f' \) is given as \( 0 \), indicating that there are no points where the slope of the function changes. This suggests that \( f \) may be a constant function, which does not have any relative minima or maxima.

Since \( f' = 0 \) and there are no critical points found, we conclude that there are no points at which \( f \) has a relative minimum.

The second derivative \( f'' \) is also \( 0 \). This further confirms that the function does not exhibit any curvature that would indicate the presence of a relative minimum.

Final Answer