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Let f(x)=a/x+x^2dot If it has a maximum ...

Let `f(x)=a/x+x^2dot` If it has a maximum at `x=-3,` then find the value of `adot`

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`f(x) =(a)/(x^(2))+2x`
For `f(x)=0,x^(3)=(a)/(2)`
For x=-3,a=-(54)
Now f(x)=`(2a)/(x^(3))+2`
`f(-3)=-(108)/(3^(3))+2=6gt0`
So, f(x)has minima at x =-3 if a =-54
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