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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
The function $f(x) = {x^3} - 3{x^2} - 24x + 5$ is an increasing function in the interval given below
  • ✓
    $( - \infty ,\, - 2) \cup (4,\infty )$
  • B
    $( - 2,\infty )$
  • C
    $(-2, 4)$
  • D
    $( - \infty ,\,4)$
✓

Answer

Correct option: A.
$( - \infty ,\, - 2) \cup (4,\infty )$
a
(a) $f(x) = {x^3} - 3{x^2} - 24x + 5$

For increasing, $f'(x) > 0$ ==> $3{x^2} - 6x - 24 > 0$

==> ${x^2} - 2x - 8 > 0$

${x^2} - 4x + 2x - 8 > 0$ ==> $(x + 2)(x - 4) > 0$

$x \in ( - \infty ,\, - 2) \cup (4,\infty )$.

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