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)=6 and p(3)=2 , then p^ (0) is

Step-by-step solution

Since, p(x) has a local maximum at x=1 and a local minimum at x=3 and p(x) is a real polynomial of least degree. Hence, let p^ (x)=k(x-1)(x-3)=k (x²-4 x+3 ) p(x)=k ( x³ 3 -2 x²+3 x )+c Now, p(1)=6 and p(3)=2 array l 4 3 k+C=6 and 0+C=2 k=3 p^ (x)=3(x-1)(x-3) p^ (0)=9 array