The minimum of the function f(x) = 2x^3 - 21x^2 + 36x - 20 is : - Vidyadip

MCQ

The minimum of the function $f(x) = 2x^3 - 21x^2 + 36x - 20$ is :

✓
$-128$
B
$-126$
C
$-120$
D
none of these.

✓

Answer

Correct option: A.

$-128$

$f(x) = 2x^3 - 21x^2 + 36x - 20$
$\Rightarrow f'(x) = 6x^2- 42x + 36$
For local maxima or minima
$6x^2 - 42x + 36 = 0$
$x^2 - 7x + 36 = 0$
$\Rightarrow x = 1 or x = 6$
$f''(x) = 12x - 42$
$\Rightarrow f''(1) = -30 < 0$
Also, $f''(6) = 30 > 0$
function has minima at $x = 6$
$\Rightarrow f(6) = -128$

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