The interval for which the given function f(x) = 2 x^3 - 3 x^2 - … - Vidyadip

MCQ

The interval for which the given function $f(x) = 2{x^3} - 3{x^2} - 36x + 7$ is decreasing, is

✓
$(-2, 3)$
B
$(2, 3)$
C
$(2,-3)$
D
None of these

✓

Answer

Correct option: A.

$(-2, 3)$

a
(a) $f(x) = 2{x^3} - 3{x^2} - 36x + 7$

$ \Rightarrow f'(x) = 6{x^2} - 6x - 36$ but for decreasing $f'(x) < 0$

==> ${x^2} - x - 6 < 0 \Rightarrow (x - 3)(x + 2) < 0$ ==> $ - 2 < x < 3$

Hence the required interval is $ (-2, 3).$

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