If the function f(x)=2 x^2-k x+5 is increasing on [1, 2], then k lies…

We have, f'(x) = 4x - k

Since f(x) is an increasing function on [1, 2]. Therefore,

$f'(x)>0$ for $1 \leq x \leq 2$

Now,

f''(x) = 4 for all $x \in[1,2]$

⇒ f''(x) > 0 for all $x \in[1,2]$

⇒ f'(x) is an increasing function on [1, 2]

⇒ f'(1) is the least value of f'(x) on [1, 2]

Therefore, for f'(x) to be greater than zero for all $x \in[1,2]$ its least value i.e.

f'(1) must also be greater than zero.

Now, $f'(1)>0 \Rightarrow 4-k>0 \Rightarrow k<4 \Rightarrow k \in(-\infty, 4)$