If the function f(x) = 2x^2 - kx +7, is increasing on [1, 2], then k…

The correct answer is Option (2) → $(-∞, 4)$

$f(x)=2x^2 - kx + 7$

For $f(x)$ to be increasing on $[1,2]$, the derivative must satisfy:

$f'(x) \ge 0$ on $[1,2]$

Compute derivative:

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

Minimum value of $4x - k$ on $[1,2]$ occurs at $x=1$:

$4(1) - k \ge 0$

$4 - k \ge 0$

$k \le 4$

Therefore:

$k \le 4$