For which interval, the function `(x^2-3x)/(x-1)` satisfies all the conditions of Rolle's theorem

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

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 -

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

The function f(x) = x(x+3) e^(-x/2) satisfies all the conditions of Rolle's theorem on (-3,0) . Find the value of c such that f'(c) = 0

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