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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions1 Mark
Question
If the function f(x) = 2x2 - kx + 5 is increasing on [1, 2], then k lies in the interval:
  1. $(-\infty,4)$
  2. $(4,\infty)$
  3. $(-\infty,8)$
  4. $(8,\infty)$
✓

Answer

  1. $(-\infty,4)$

Solution:

f(x) = 2x2 - 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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