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Let p(x) be a real polynomial of least d...

Let `p(x)` be a real polynomial of least degree which has a local maximum at `x=1` and a local minimum at `x=3.` If `p(1)=6a n dp(3)=2,` then `p^(prime)(0)` is_____

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The correct Answer is:
9
Let P(x) k(x-1)(x-3)
`therefore p(x)=k(x^(3)/(3)-2x^(2)+3x)+c`
Now `P(1)=6 rarr4/3k+c=6`
Also `P(3)=2rarrc=2`
So k = thus p(0)=3x=9
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