If $f(x) = x^2 - 4x + 13, x ∈R$,then which of the following are correct?

(A) $x = 2$ is a stationary point of f(x).
(B) f(x) is increasing function on $(2,∞)$
(C) f(x) have maxima at $x = 2$
(D) $f(2) = 9$

Choose the correct answer from the options given below:

(A), (B) and (D) only

The correct answer is Option (4) → (A), (B) and (D) only **

Given:

$f(x) = x^{2} - 4x + 13$

Differentiate:

$f'(x) = 2x - 4$

Set derivative zero:

$2x - 4 = 0$

$x = 2$

So (A) is correct.

Second derivative:

$f''(x) = 2 > 0$

This means $x=2$ is a point of minima, NOT maxima → (C) is false.

Since the parabola opens upward, the function is increasing for $x > 2$ → (B) is correct.

Compute $f(2)$:

$f(2) = 4 - 8 + 13 = 9$

So (D) is correct.

Correct options: (A), (B), (D)