If the function f(x)=x^2-k x+5 is increasing on [2,4], then: - Vidyadip

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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