Let f(x) = 2x^3 - 3x^2 - 12x + 5 on [-2, 4]. The relative maximum… - Vidyadip

MCQ

Let $f(x) = 2x^3 - 3x^2 - 12x + 5$ on $[-2, 4].$ The relative maximum occurs at $x =$

A
$-2$
B
$-1$
✓
$2$
D
$4$

✓

Answer

Correct option: C.

$2$

Given, $f(x) = 2x^3 - 3x^2 - 12x + 5$
$\Rightarrow f'(x) = 6x^2 - 6x - 12$
For a local maxima or a local minima, we must have $f'(x) = 0$
$\Rightarrow 6x^2 - 6x - 12 = 0$
$\Rightarrow x^2- x - 2 = 0$
$\Rightarrow (x - 2)(x + 1) = 0$
$\Rightarrow x = 2, -1$
Now, f$''(x) = 12x - 6$
$\Rightarrow f''(-1) = -12 - 6 = 18 > 0$
So, $x = 1$ is a local maxima.
Also, $f''(2) = 24 - 6 = 18 > 0$
So, $x = 2$ is a local minima.

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