Does the function `f(x)=3x^(2)-5` satisfy the conditions of the Lagrange theorem in the interval `[-2,0]` ? If it does then find the point `xi` in the Lagrange formula `f(b)-f(a)=f'(xi)(b-a)`.

Does the function f(x) = {:{(x" if "x lt 1),(1//x " if "x ge1):} satisfy the conditions of the Lagrange theorem on the interval [0,2] ?

The point where the function f(x)=x^(2)-4x+10 on [0,4] satisfies the conditions of Rolle's theorem is

If the function f(x)=x^3-6x^(2)+ax+b satisfies Rolle's theorem in the interval [1,3] and f'((2sqrt(3)+1)/(sqrt(3)))=0 , then

If the function f(x) = x^(3) – 6ax^(2) + 5x satisfies the conditions of Lagrange’s mean theorem for the interval [1, 2] and the tangent to the curve y = f(x) at x = 7//4 is parallel to the chord joining the points of intersection of the curve with the ordinates x = 1 and x = 2 . Then the value of a is

If the function f(x) = x^(3) - 6x^(2) + ax + b satisfies Rolle's theorem in the interval [1,3] and f'[(2sqrt(3)+1)/sqrt(3)]=0 , then a=

The constant c of Lagrange’s theorem for f(x)=(x)/(x-1)" in "[2,4]" is :"

Apply the Lagrange formula to the function f(x) = In x in the interval [1,e] and find the corresponding of xi .

The constant c of Lagrange's theorem for f(x)=x^(3)-4x^(2)+4x in [0,2]