What is the x-value of the relative minimum on the graph of f(x)
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(1 point)
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Without the function f(x) provided, it is not possible to determine the x-value of the relative minimum on the graph of f(x).
To find the x-value of the relative minimum on the graph of f(x), you need to locate the point where the graph reaches its lowest point.
To do this, we can analyze the function's derivative.
Step 1: Find the derivative of f(x) using the rules of differentiation.
Step 2: Set the derivative equal to zero and solve for x to find critical points.
Step 3: Use the second derivative test to determine whether the critical point is a relative minimum.
Step 4: If the critical point is a relative minimum, the x-value of that point is the answer.
Without the specific function f(x), it is not possible to provide a more detailed step-by-step explanation.
To find the x-value of the relative minimum on the graph of f(x), you need to find the critical points and then evaluate them to identify the minimum point.
1. Calculate the derivative of f(x) to find the critical points. The critical points occur where the derivative is equal to zero or undefined.
2. Set the derivative equal to zero and solve for x. This will give you the x-coordinate(s) of the critical point(s).
3. Evaluate the second derivative of f(x) at each critical point to determine the nature of the extremum (minimum or maximum).
4. If the second derivative is positive, then the critical point represents a relative minimum. If the second derivative is negative, then it represents a relative maximum.
5. Plug in the x-coordinate(s) of the critical point(s) into the original function f(x) to get the y-coordinate(s) of the relative minimum(s).
The x-value of the relative minimum is the x-coordinate(s) obtained in step 2.