What is the x-value of the relative minimum on the graph of f(x)
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To determine the x-value of the relative minimum on the graph of f(x), we need more information about the function f(x). Without knowing the specific function, we cannot determine the x-value of the relative minimum.
To find the x-value of the relative minimum on the graph of f(x), we need to use calculus.
Step 1: Take the derivative of the function f(x) to find the critical points. Critical points are the x-values where the derivative is either zero or undefined.
Step 2: Set the derivative equal to zero and solve for x.
Step 3: Once you have the x-values of the critical points, substitute them into the second derivative to determine if they correspond to a relative minimum or maximum.
Step 4: If the second derivative is positive at a critical point, it corresponds to a relative minimum. So, find the x-value of the relative minimum.
To find the x-value of the relative minimum on the graph of the function f(x), you can follow these steps:
1. Determine the critical points of the function by finding the values of x where the derivative of f(x) is equal to zero or undefined.
2. Calculate the second derivative of f(x) to determine the concavity of the graph. The second derivative can be found by taking the derivative of the first derivative of f(x).
3. Determine the intervals where the function is increasing or decreasing by analyzing the sign of the first derivative.
4. Identify the intervals where the function changes from decreasing to increasing or vice versa. These intervals will correspond to possible relative minimum or maximum points.
5. Test the critical points and the endpoints of the given interval(s) by substituting them into the original function f(x). Compare the values obtained to determine the relative minimum or maximum.
By following these steps, you should be able to find the x-value of the relative minimum on the graph of f(x).