Finding the Real Roots of a Cubic Function

Very Hard Passport To Advanced Math Non-linear Expressions

Consider the function defined by the equation:

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

To find the number of real solutions to the equation $$f(x) = 0$$, you need to analyze the roots of the cubic polynomial. Specifically, what can you infer about the real roots of this polynomial based on its derivative?

There is one real root.

There are two real roots.

There are three real roots.

There are no real roots.

Hint

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