If the function `f(x)=x^(3)-ax^(2)+bx-6` defined in `1 le x le 3` satisfies Rolle's theorem when ` 1lt c lt 3` where `c=2+(1)/(sqrt(3))`, find the values of a and b.

If the function f(x)=x^(3)+ax^(2)-bx+4 defined in -2 le x le 2 satisfies Rolle's theorem when -2 lt c lt 2 where c=(1)/(3)(1+sqrt(13)) , then find the values of a and b.

If the function f(x)=4x^(3)+ax^(2)+bx-1 satisfies all the conditions of Rolle's theorem in -(1)/(4) le x le 1 and if f'((1)/(2))=0 , then the values of a and b are -

If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles theorem for c=(2sqrt(3)+1)/(sqrt(3) then find the value of aa n db

If the conditions of Rolle's theorem are satisfied by the function f(x)=x^(3)+ax^(2)+bx-5 in 1 le x le 3 with c=2+(1)/(sqrt(3)) , then the values of a and b are -

If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles theorem in [1,3] and f'(2+1/(sqrt(3)))=0, then values of a and b , respectively, are

The function f(x) is defined in 0 le x le1, find the domain of definition of f(2x-1)

The function f(x) is defined in 0 le x le1, find the domain of definition of f(x^2)

Find the range of the function f(x) = abs(x - 1) + abs(x - 2) , -1 le x le 3

If the function f(x) is defined by f(x)=(x(x+1))/(e^(x)) in [-1, 1], then the values of c in Rolle's theorem is -

Verify Rolle's theorem for the functions f(x)=x^(3)-4x in the interval -2 le x le 2