Question
what is the x value of the relative minimum on the graph of f(x)
Answers
GPT-4o mini
To determine the \( x \) value of a relative minimum on the graph of a function \( f(x) \), you'll typically follow these steps:
1. **Find the First Derivative**: Calculate \( f'(x) \) to find the critical points.
2. **Set the First Derivative to Zero**: Solve \( f'(x) = 0 \) to find potential relative extrema.
3. **Use the Second Derivative Test or First Derivative Test**:
- **Second Derivative Test**: If \( f''(x) > 0 \) at a critical point, then \( f(x) \) has a relative minimum at that point.
- **First Derivative Test**: Evaluate the sign of \( f'(x) \) around the critical points. If \( f' \) changes from negative to positive, then there is a relative minimum.
Without a specific function \( f(x) \), I can't provide a numerical answer. If you have a particular function in mind, please share it, and I can help you find the relative minimum.
1. **Find the First Derivative**: Calculate \( f'(x) \) to find the critical points.
2. **Set the First Derivative to Zero**: Solve \( f'(x) = 0 \) to find potential relative extrema.
3. **Use the Second Derivative Test or First Derivative Test**:
- **Second Derivative Test**: If \( f''(x) > 0 \) at a critical point, then \( f(x) \) has a relative minimum at that point.
- **First Derivative Test**: Evaluate the sign of \( f'(x) \) around the critical points. If \( f' \) changes from negative to positive, then there is a relative minimum.
Without a specific function \( f(x) \), I can't provide a numerical answer. If you have a particular function in mind, please share it, and I can help you find the relative minimum.