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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
If the absolute maximum value of the function $f ( x )$ $=\left( x ^{2}-2 x +7\right) e ^{\left(4 x^{3}-12 x ^{2}-180 x +31\right)}$ in the interval $[-3$, $0]$ is $f (\alpha)$, then.
  • A
    $\alpha=0$
  • ✓
    $\alpha=-3$
  • C
    $\alpha \in(-1,0)$
  • D
    $\alpha \in(-3,-1)$
✓

Answer

Correct option: B.
$\alpha=-3$
b
$f^{\prime}(x)=e^{\left(4 x^{2}-12 x^{2}-180 x+31\right)}(12\left(x^{2}-2 x+7\right)$

$(x+3)(x-5)+2(x-1)$

for $x \in[-3,0]$

$f ^{\prime}( x )<0$

$f ( x )$ is decreasing function on $[-3,0]$

The absolute maximum value of the function $f(x)$ is at $x=-3$

$\alpha=-3$

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