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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions1 Mark
MCQ
If the function $f(x) = 2x^2 - kx + 5$ is increasing on $[1, 2]$, then $k$ lies in the interval :
  • ✓
    $(-\infty,4)$
  • B
    $(4,\infty)$
  • C
    $(-\infty,8)$
  • D
    $(8,\infty)$
✓

Answer

Correct option: A.
$(-\infty,4)$
$f(x) = 2x^2 - kx + 5$
$f\ '(x) = 4x - k$
$f(x)$ is increasing
$4x - k < 0$ on $[1, 2]$
$k < 4x$
Minimum value of $k$ is $4.$
$k < 4$
$\text{k}\in(-\infty,4)$

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