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

MCQ

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

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

✓

Answer

Correct option: A.

$-128$

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

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