Verify Lagrange's mean value theorem in the interval [a,b] if
(i) `f(x) = x^2+x-1,a = -1,b=1`

Verify Lagrange's mean value theorem in the interval [a,b] if (ii) f(x) = x^2-4x-3,a=1,b=4

Verify Lagrange's mean value theorem in the interval [a,b] if (iv) f(x) = x+1/x,a=1, b=3

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

Find the greatest value of x^2 log x in the interval [1,e]

Find the domain and range of f if . f(x)=1/(x^2-1)

Show that the Rolle's theorem is not applicable for f(x) = x^(1/3) on [-1,1]

Find the domain and range of f if . f(x)=1/(x(x-1))

Verify Rolle's theorem for (i) f(x) =x^2-5x+4 on [1,4]

Verify the identify (x+a)(x+b) = x2 +(a+b)x+ab, for a =2,b=3, x=5