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_____

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

If P (x) be a polynomial of degree three that has a local maximum value 8 at x=1 and a local minimum value 4 at x=2 , then p (0 ) is equal to :

Let f(x) be a cubic polynomial which is having local maximum at (1,2) and f'(x) has local extrema at x=0 .If f(0)=1 then

Let g (x) be a cubic polnomial having local maximum at x=-1 and g '(x) has a local minimum at x =1, If g (-1) =10 g, (3) =- 22, then

Consider a polynomial P(x) of the least degree that has a maximum equal to 6 at x=1 and a minimum equal to 2 at x=3. Then the value of p(2)+P(0)-7 is

If P(x) is a polynomial of the least degree that has a maximum equal to 6 at x=1, and a minimum equalto 2 at x=3, then int_(0)^(1)P(x)dx equals:

Let P(x) be a real polynomial of degree 3 which vanishes at x=-3. Let P(x) have local minima at x=1, local maximum at x=-1 and underset(-1)overset(1)int P(x)dx=-18 , then the sum of all the coefficients of the polynomical P(x) is equal to........