Find the maximum and minimum values, if any, of the following functions given by
(i) `f(x)=(2x-1)^2+3`
(ii) `f(x)=9x^2+12 x+2`
(iii) `f(x)=-(x-1)^2+10`
(iv) `g(x)=x^3+1`

Explanation

Let's solve the given functions step by step to find their maximum and minimum values.

### (i) \( f(x) = (2x - 1)^2 + 3 \)

1. **Identify the nature of the function**: The term \( (2x - 1)^2 \) is a square term, which is always non-negative. The minimum value of \( (2x - 1)^2 \) is 0, which occurs when \( 2x - 1 = 0 \) or \( x = \frac{1}{2} \).

2. **Calculate the minimum value**:
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