State Rolle’s theorem.

It is given that Rolle’s theorem holds for the function f(x)=x^(3)+bx^(2)+ax on [1,3] with C = 2+(1)/sqrt(3) . Find the values a and b

Verify whether Rolle’s theorem is applicable to f(x) = tanx on [(pi)/(4),(5pi)/(4)] ?

Find “c” of the Rolle’s theorem for f(x)=log(x^(2)+ab)/(a+bx) in [a, b] where a, b gt 0.

Find “ theta ” of the Rolle’s theorem for the function f(x ) = x^(2) -5x + 7 in [2,3], at least one root atmost one root

Function for which LMVT is applicable but Rolle’s theorem is not

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? f(x) = [x] for x in [-2,2]

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? f(x) = [x] for x in [5,9]

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle’s theorem from these example? f(x) = x^2 -1 for x in [1,2]

Verify Rolle’s theorem for the function y = x^2 +2 , a = -2 and b = 2

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