The function `f(x) = x(x+3) e^(-x/2)` satisfies all the conditions of Rolle's theorem on `(-3,0)`. Find the value of `c` such that `f'(c) = 0`

If the function f(x)= e^x(sinx-cosx), x in [(pi)/4, (5pi)/4] satisfies all the conditions of the Rolle's theorem, then the value of c is...... A) 0 B) pi C) pi/2 D) pi/4

If f(x) satisfies the condition for Rolle's theorem on [3,5] then underset(3) overset(5)int f(x) dx equals

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) =log x, x in (1, e) , satisfies all the conditions of LMVT, then the value of c is..... A) 1 B) e C) 1/e D) e-1

If the function f(x) = ax^3 + b x^2+11x - 6 satisfies conditions of Rolle's theorem in [1, 3] and f’(2+ (frac{1}{sqrt 3})) = 0, then values of a and b are respectively

For the function f(x)=e^cosx , 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

Check whether conditions of Rolle's theorem are satisfied by the following functions: f(x) = x^2 - 2x + 3, x in (1,4)