The function `f(x)=x^(3)-6x^(2)+ax+b` satisfy the conditions of Rolle's theorem in `[1,3]` .The values of `a` and `b` are

The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle's theorem in (-3,0). The value of c, is

The function f(x) =x^(3) - 6x^(2)+ax + b satisfy the conditions of Rolle's theorem on [1,3] which of these are correct ?

If f(x)=x^(3)+bx^(2)+ax satisfies the conditions on Rolle's theorem on [1,3] with c=2+(1)/(sqrt(3))

If the function f(x)=ax^(3)+bx^(2)+11x-6 satisfies condition of Rolle's theorem in [1, 3] for x=2+(1)/(sqrt(3)) then value of a and b are respectively (A) 1, -6 (B) 2, -4 (C) 1, 6 (D) None of these.

If the function f(x)=ax^(3)+bx^(2)+11x-6 satisfies conditions of Rolles theorem in [1,3] for x=2+(1)/(sqrt(3)), then values of a and b respectively,are -3,2(b)2,-41,6(d) none of these

The point where the function f(x)=x^(2)-4x+10 on [0,4] satisfies the conditions of Rolle's theorem is

it is given for the function f(x)=x^(3)-6x^(2)+ax+b on [1,3], Rolle's theorem holds with c=2+(1)/(sqrt(3)). Find the values of a and b if f(1)=f(3)=0

If the function f(x) = x^(3) – 6ax^(2) + 5x satisfies the conditions of Lagrange’s mean theorem for the interval [1, 2] and the tangent to the curve y = f(x) at x = 7//4 is parallel to the chord joining the points of intersection of the curve with the ordinates x = 1 and x = 2 . Then the value of a is