Verify LMVT for the following functions on the intervals shown against them and find the possible values of c :
`f(x)=x(x+4)^(2), x in [0, 4]`

Verify LMVT for the following functions on the intervals shown against them and find the possible values of c : f(x)=logx, x in [1, e] .

Verify LMVT for the following functions: f(x) = x+1/x , x in (1,3)

Verify LMVT for the following functions: f(x)=x(2-x),x in[0,1]

Verify LMVT for the following function f(x)=x+(1)/(x),x in[1,3]

Verify Lagrange's mean value theorem for the following functions in the given interval and also find 'c' of this theorem: f(x) = (x-1)(x-2)(x-3) in[0,4]

Verify Lagrange's mean value theorem for the following functions in the given interval and also find 'c' of this theorem: f(x) = x^(2//3) in [0,1]

Verify Lagrange's mean value theorem for the following functions in the given interval and also find 'c' of this theorem: f(x) = sqrt(x^2-4) in [2,4]

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

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

Verify Lagrange's mean value theorem for the following functions in the given interval and also find 'c' of this theorem: f(x) = x(x-3) in [2,4]