Verify mean value theorem for the function `f(x)=x^(2)` on [2,4]

The constant c of the Lagrange's mean value theorem for the function f(x)=1+x^2 on [1,2] is

Verify the conditions of Lagrange's mean value theorem for the function x^2-1 on [2,3]

The value of theta of mean value theorem for the function f(x) = ax^(2) + bx + c in [1,2] is

Verify Rolle's theorem for the function y=f(x)=x^2+4 on [-3,3]

Verify Rolle's theorem for the function f(x)=x(x+3)e^(-x/2) in [-3,0].

Verify Rolle's theorem for the functions f(x)=x(x+3)e^(-x//2) on [-3,0]

Verify Rolle's theorem for the functions (x^(2)-1)(x-2) on [-1,2]. Find the point in the interval where the derivative vanishes.