Verify Lagrange's Mean Value Theorem for the following function:
`f(x)=2sin x+sin2x` on `[0,pi]`.

f(x) = sinx - sin2x in [0,pi]

Verify Rolle's theorem for the following function f(x)=e^(-x) sin x in [0,pi]

Verify Lagranges mean value theorem for the following function: "f"("x")=" x"^2+"2"x"+3," f o r "[4,6] .

Verify Lagrange's Mean Value theorem for the following functions in the given intervals (i) f(x) = sin x in the interval [pi//2 , 5pi//2] . (ii) f(x) = "log"_(e)x in the interval [1,e].

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = x(x+2)^(2) in the interval [0,2]

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = e^(x) in the interval [0,1].

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = 1 + 2x -x^(2) in the interval [0,1] .

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = x^(2) + x -2 in the interval [0,4] .

Verify Lagrange's Mean Value Theorem for the function f(x)=sqrt(x^(2)-x) in the interval [1,4] .

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = (x-2) (x-3) (x-4) , in the interval [2,5]/