Verify Mean Value Theorem, if `f(x)=x^2-4x-3`in the interval [a, b], where `a = 1 a n d b = 4`.

Verify Mean Value Theorem, if f(x)= x^(2)-4x-3 in the interval [a, b] where a=1 and b= 4.

Verify Mean Value Theorem, if f(x)= x^(3)-5x^(2)-3x in the interval [a, b], where a=1 and b=3. Find all c in (1,3) for which f'(c )= 0

Verify Mean Value Theorem for the function f(x)= x^(2) in the interval [2, 4].

Verify Mean value Theorem for the function f(x)= x^(2) in the interval [2,4]

Verify Rolle's theorem for the function f(x)= x^(2) + 2x-8, x in [-4, 2]

Consider the polynomial function f(x)=x^7/7-x^6/6+x^5/5-x^4/4+x^3/3-x^2/2+x Statement-1: The equation f(x) = 0 can not have two or more roots.Statement-2: Rolles theorem is not applicable for y=f(x) on any interval [a, b] where a,b in R

Verify mean value theorem for each of the functions: f(x) = (1)/(4x-1), x in [1, 4]

Vertify mean value theorem for the following functions: f(x)= x^(2) + 2x+ 3, x in [4, 6]