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  1. x=-3 is a point of local minima

  2. x=-3 is a point of local maxima

  3. x=0 is a point of local maxima

  4. x=0 is a point of local minima


Solution

The correct option is A

x=-3 is a point of local minima


To find local maxima or minima we need to differentiate f(x) with respect to x we obtain

f'(x)=3x2ex + x3 e= x2ex (3+x)         

roots of f'(x)=0 are x=0,x=-3

Now f'(x) does not changes its sign as x passes through x = 6

So x=0 is a point of inflection and f'(x) changes sign from negative to positive as x passes through x =-3 so it comes out to be a point of local minima.

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