Verify the truth of Lagrange's mean value theorem formula for the following functions :
`f(x)=x(x-1)(x-2)" in "[0, (1)/(2)]`

Verify the truth of Lagrange's mean value theorem formula for the following functions : f(x)=x^(2)+x-1" in " [0, 4]

Verify the truth of Lagrange's mean value theorem formula for the following functions : f(x)=sqrt(x^(2)-4)" in " [2, 4]

Verify the truth of Lagrange's mean value theorem formula for the following functions : f(x) =x^(3)-2x^(2)-x+3" in " [0, 1]

Verify the truth of Lagrange's mean value theorem formula for the following functions : f(x)=x(x+4)^(2)" in " 0 le x le 4

Verify the truth of Lagrange's mean value theorem formula for the following functions : f(x)=(x-1)(x-2)(x-3)" in " 0 le x le 4

Verify the truth of Lagrange's mean value theorem formula for the following functions : f(x)=x^(2)-4x-3 in the interval 0 le x le 4 .

Verify the truth of Lagrange's mean value theorem formula for the following functions : 2sin x+sin 2x" in " 0 le x le pi

Verify Lagrange's mean value theorem for the following functions: f(x) = (x-1)(x-2)(x-3) on [0,4]

Verify Lagrange's mean-value theorem for each of the following functions f(x) = e^(x) " on " [0, 1]