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

MCQ

If the function $f(x) = x^2 - kx + 5$ 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.

$\text{k}\in(-\infty,4)$

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

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