Find the maximum and the minimum values of `f(x)=x^3+1` for all `x in R` , if any.

Explanation

To find the maximum and minimum values of the function \( f(x) = x^3 + 1 \) for all \( x \in \mathbb{R} \), we will follow these steps:

### Step 1: Analyze the function
The function \( f(x) = x^3 + 1 \) is a cubic polynomial. Cubic functions generally have the form \( ax^3 + bx^2 + cx + d \) and can have one or two turning points depending on the coefficients.

**Hint:** Consider the general behavior of cubic functions. They can increase or decrease without bound.

### Step 2: Find the derivative
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