Verify Rolle's theorem for the functions `f(x)=x(x+3)e^(-x//2)` on [-3,0]

Verify Rolle's theorem for the function f(x)=x(x+3)e^(-x/2) in [-3,0].

Verify Rolle’s theorem for the function f(x) = (x - a)m (x - b)^(n) on [a, b] where m and n are positive integers.

Verify Rolle's theorem for the functions (x^(2)-1)(x-2) on [-1,2]. Find the point in the interval where the derivative vanishes.

Verify Rolle's theorem for the function y=f(x)=x^2+4 on [-3,3]

Verify Rolle's theroem for the function x^2-1 on [-1,1] .

Find c of the R olle’s theorem for the functions f(x)=log(x^(2)+3)/(4x) in [1,3]