The interval of the decreasing function f(x) = x^3 - x^2 - x - 4 … - Vidyadip

MCQ

The interval of the decreasing function $f(x) = {x^3} - {x^2} - x - 4$ is

A
$\left( {{1 \over 3},\,1} \right)$
✓
$\left( { - {1 \over 3},1} \right)$
C
$\left( { - {1 \over 3},\,{1 \over 3}} \right)$
D
$\left( { - 1, - {1 \over 3}} \right)$

✓

Answer

Correct option: B.

$\left( { - {1 \over 3},1} \right)$

b
(b) Given $f(x) = {x^3} - {x^2} - x - 4$

This function will be decreasing function when $f'(x) < 0$

==> $3{x^2} - 2x - 1 < 0 \Rightarrow 3{x^2} - 3x + x - 1 < 0$

==> $(3x + 1)(x - 1) < 0$;

$\therefore 3x + 1 > 0$ and $x - 1 < 0$

$x > - \frac{1}{3}$ and $x < 1$;

$\therefore x \in \left( {\frac{{ - 1}}{3},\,1} \right)$

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