f(x)=x(x-4)^(2)" in the interval "[0,4]

Verify the truth of Rolle's Theorem for the following functions : f(x)=(x-2)(x-4)^(2) in the interval [2, 4].

Verify Rolle's theorem for the following functions f(x)=(x-2)(x-4)^2 in the interval [2, 4]

Statement - 1 : Rolle's Theorem can be applied to the function f(x)=1+(x-2)^(4//5) in the interval [0, 4] and Statement - 2 : f(x) is continuous in [0, 4] and f(0)=f(4) .

Verify Lagrange's mean theorem for the function f(x) =x^(2) + x-1 in the interval [0,4]

Verify Lagrange's mean theorem for the function f(x) =x^(2) + x-1 in the interval [0,4]

Verify Rolle's theorem for the function f(x)=x^(2)-4x-3 , in the interval [1,4].

Using Lagrange's theorem , find the value of c for the following functions : (i) x^(3) - 3x^(2) + 2x in the interval [0,1/2]. (ii) f(x) = 2x^(2) - 10x + 1 in the interval [2,7]. (iii) f(x) = (x-4) (x-6) in the interval [4,10]. (iv) f(x) = sqrt(x-1) in the interval [1,3]. (v) f(x) = 2x^(2) + 3x + 4 in the interval [1,2].

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 following functions in the given intervals f(x) = x^(2) + x -2 in the interval [0,4] .

Find the value of c, of mean value theorem.when (a) f(x) = sqrt(x^(2)-4) , in the interval [2,4] (b) f(x) = 2x^(2) + 3x+ 4 in the interval [1,2] ( c) f(x) = x(x-1) in the interval [1,2].