Find the points of local maxima and local minima, if any, of the following functions. Find also the local maximum and local minimum values :
The constant function ` alpha`.

Answer

To find the points of local maxima and local minima for the constant function \( f(x) = \alpha \), we will follow these steps:

### Step 1: Define the Function
Let \( f(x) = \alpha \), where \( \alpha \) is a constant.

### Step 2: Find the Derivative
To find the critical points, we first need to compute the derivative of the function:
\[ f'(x) = 0 \]
Since \( \alpha \) is a constant, the derivative of any constant is zero.

### Step 3: Set the Derivative to Zero
Next, we set the derivative equal to zero to find critical points:
\[ f'(x) = 0 \]
This means that there are no values of \( x \) that will yield a critical point since \( f'(x) \) is always zero.

### Step 4: Analyze the Critical Points
Since there are no critical points, we conclude that the function does not have any local maxima or minima.

### Step 5: Conclusion
Thus, we can state that:
- The function \( f(x) = \alpha \) has neither local maxima nor local minima.
- The value of the function is always \( \alpha \) for any value of \( x \).

### Final Answer
The function \( f(x) = \alpha \) has neither local maxima nor local minima.

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