Finding Minimum Value of Function

Very Hard Algebra Functions

Let the function $$ f(x) $$ be defined as follows:

$$ f(x) = x^3 - 6x^2 + 9x + 1 $$

Determine the value of $$ x $$ for which the function $$ f(x) $$ has a minimum value, and then find $$ f(x) $$ at that point.

The minimum value is $$ -1 $$ at $$ x = 3 $$.

The minimum value is $$ 1 $$ at $$ x = 2 $$.

The minimum value is $$ 3 $$ at $$ x = 1 $$.

The minimum value is $$ 0 $$ at $$ x = 0 $$.

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