Verify LMV theorem : `f(x) = x (x - 2) in [1, 3]`.

Verify Rolle's theorem for f(x)= x, x in [1,2]

Verify Lagrange's mean value theorem for the following functions in the given interval and also find 'c' of this theorem: f(x) =( x)(x-1) (x-2) in [0,1/2]

Verify Rolle's theorem for f (x) = x^2 - 3x + 2, x in [1, 2]

Verify Rolle's theorem for f (x) = x^2 - 8x + 15, x in [3, 5]

Verify Lagrange's mean value theorem for the following functions in the given interval and also find 'c' of this theorem: f(x) = x(x-3) in [2,4]

Verify Rolle's theorem for f (x) = x^2 - 9x + 14, x in [2, 7]

Verify Lagrange's mean value theorem for the following functions in the given interval and also find 'c' of this theorem: f(x) = (x-1)(x-2)(x-3) in[0,4]

Verify Mean Value Theorem, if f(x) = x^2-4x-3 , in the interval [a, b], where a = 1 and b = 4.

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