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:
Answer & explanation
Correct answer: option 4
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)