Let $f(x) = x^3 - 6x^2 + 9x - 8$ be a function, then which of the following statements are TRUE?

(A) $f'(x) = 3(x - 1)(x - 3)$

(B) The critical points of the function are $x = 1$ and $x = 3$

(C) $x = 1$ is the point of local minimum

(D) The local maximum value is $-4$

Choose the correct answer from the options given below:

Given: $f(x) = x^3 - 6x^2 + 9x - 8$

The first derivative is:

$f'(x) = 3x^2 - 12x + 9$

$f'(x) = 3(x^2 - 4x + 3)$

$f'(x) = 3(x - 1)(x - 3)$

Statement (A) is TRUE.

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For critical points, set $f'(x) = 0$:

$3(x - 1)(x - 3) = 0$

$(x - 1)(x - 3) = 0$

The critical points are $x = 1$ and $x = 3$.

Statement (B) is TRUE.

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The second derivative is:

$f''(x) = 6x - 12$

At $x = 1$:

$f''(1) = 6(1) - 12$

$f''(1) = -6$

Since $f''(1) < 0$, the point $x = 1$ is a local maximum.

Statement (C) is FALSE.

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The local maximum value at $x = 1$:

$f(1) = (1)^3 - 6(1)^2 + 9(1) - 8$

$f(1) = 1 - 6 + 9 - 8$

$f(1) = -4$

Statement (D) is TRUE.

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The true statements are (A), (B), and (D).