Verify Rolle's Theorem for the function f which is defined by `f(x) = x^2 - 4x + 3, x in [1, 3]`.

Verify Rolle's Theorem for the function f which is defined by f(x) = x^2 - 5x + 4, x in [1, 4] .

Verify Rolle's Theorem for the function f which is defined by f(x) = x^2 + 2x - 8, x in [-4, 2] .

Verify Rolle's theorem for the function given by : f(x) = x^2 - 10x + 21 , x in [3, 7]

Verify Rolle's theorem for the function given by : f(x) = x^2 + 2x - 8 , x in [- 4, 2]

Verify Rolle's theorem for the function given by : f(x) = x^2 + 5x + 4 , x in [1, 4]

Verify Rolle's Theorem for the function: f(x) = sin x+cos x in [0,pi/2]

Verify Lagrange's Mean Value Theorem for the function f defined by f(x) = x^3 + x^2 - 6x in the interval [-1,4]

Verify Rolle's Theorem for the function: f(x) = sin x + cos x -1 in [0,pi/2]

Verify Rolle's theorem for the function : f(x) = x^3-3x^2 + 24x - 80 in the interval [-4, 5]

Verify Rolle's Theorem for the following functions : f(x) = (x^2 - 1) (x - 2) in [- 1, 2]