The function f(x) = x^3 - 3 x^2 - 24x + 5 is an increasing functi… - Vidyadip

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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