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  • If the absolute maximum value of the function  <img alt="\mathrm{f(x)=\left(x^{2}-2 x+7\right) \mathrm{e}^{\left(4 x^{3}-12 x^{2}-180 x+31\right)}}" src="/latex-image/?%5Cmathrm%7Bf%28x%29%3D%

If the absolute maximum value of the function  \mathrm{f(x)=\left(x^{2}-2 x+7\right) \mathrm{e}^{\left(4 x^{3}-12 x^{2}-180 x+31\right)}}  in the interval  \mathrm{[-3,0]} is, \mathrm{f(\alpha)} then :

Option: 1

\mathrm{\alpha=0} \\


Option: 2

\mathrm{\alpha=-3} \\


Option: 3

\mathrm{\alpha \in(-1,0)} \\


Option: 4

\mathrm{\alpha \in(-3,-1]}


Answers (1)

best_answer

\mathrm{f^{\prime}(x)=e^{\left(4 x^{3}-12 x^{2}-180 x+31\right)} \cdot\left(12\left(x^{2}-2 x+7\right)(x+3)(x-5)+2(x-1)\right)}

\mathrm{\text { for } x \in[-3,0]} \\

\mathrm{\Rightarrow \quad f^{\prime}(x)<0}

\mathrm{f(x)} is decreasing function on \mathrm{\left [ -3,0 \right ]}

The absolute maximum value of the function \mathrm{f(x)} is at \mathrm{x=-3}

\mathrm{\Rightarrow \alpha =-3}

Hence correct option is 2

Posted by

vinayak

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