MCQ
If the function $f(x)=x^2-k x+5$ is increasing on $[2,4]$, then:
  • A
    $\text{k}\in(2,\infty)$
  • B
    $\text{k}\in(-\infty,2)$
  • C
    $\text{k}\in(4,\infty)$
  • $\text{k}\in(-\infty,4)$

Answer

Correct option: D.
$\text{k}\in(-\infty,4)$
$f(x)=x^2-k x+5$
$f^{\prime}(x)=2 x-k$
Given$:\ f(x)$ is increasing on $[2,4].$
$\Rightarrow f^{\prime}(x)>0$
$\Rightarrow 2 x-k>0$
$\Rightarrow k<2 x$
$\because\ \text{x}\in[2,4],$ maximum value of $k$ is $4, k < 4.$
$\therefore\ \text{k}\in(-\infty,4)$

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