Examine the applicability of L.M.V. theorem in the interval [1, 4] of the function, `f(x) = x^2 - 4x - 3.

Discuss the applicability of Rolle's theorem for the following functions f(x) = |x - 1| , x in [0,2]

Examine the applicability of Rolle's Theorem fr the fraction: f(x) = 2+(x-1)^(2//3) in the interval 0 le x le2

Verify LMV theorem for the following functions f(x) = x^2 + x - 1 " in " [0,4]

Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2. (i) f(x) = [x] for x ∈ [5,9] (ii) f(x) = [x] for x ∈ [-2,2] (iii) f(x) = [xsqrt -1] for x ∈ [1,2]

Discuss the applicability of Rolle's Theorem for the function f(x) = (x-1)^(2//5) in the interval [0,3]

Discuss applicability of Lagrange's mean value theorem to the function f(x) = (x-1)^(2//3) in [1,2]

Discuss the applicablity of Rolle's theorem for the following functions in the indicated intervals: f(x) = x^(2//3) in[-1,1]

Verify LMV theorem for the following functions f(x) = x(x-1)(x - 2) in [0,1/2]

Discuss the applicablity of Rolle's theorem for the following functions in the indicated intervals: f(x) = (x-1)(2x-3) in [1,3]

Discuss the applicablity of Rolle's theorem for the following functions in the indicated intervals: f(x) = 3 + (x-2)^(2//3) in [1,3]