Verify Rolle's theorem for `(x-a)^m (x-b)^n` on `x in [a,b].`

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

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

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

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

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

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

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

Verify Rolle's theorem for the function f(x)=e^(x) sin 2x [0, pi/2]

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

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