what is the x value of the relative minimum on the graph of f(x)

Answer 1

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.