In which interval is the given function f(x) = 2 x^3 - 15 x^2 + 3… - Vidyadip

MCQ

In which interval is the given function $f(x) = 2{x^3} - 15{x^2} + 36x + 1$ is monotonically decreasing

A
$[2, 3]$
✓
$(2, 3)$
C
$( - \infty ,\,2)$
D
$(3,\,\infty )$

✓

Answer

Correct option: B.

$(2, 3)$

b
(b) $y = f(x) = 2{x^3} - 15{x^2} + 36x + 1$

$\frac{{dy}}{{dx}} = f'(x) = 6{x^2} - 30x + 36 = 6({x^2} - 5x + 6)$

$f'(x) = 6(x - 2)(x - 3)$

To be monotonic decreasing, $f'(x) < 0$

$ \Rightarrow (x - 2)(x - 3) < 0 \Rightarrow x \in (2,3)$.

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