If the function `f(x)=2x^2 + 3x + 5` satisfies `LMVT` at `x = 2` on the closed interval `[1, a]`, then the value of 'a' is equal to

If the function f(x)=2x^(2)+3x-m log x is monotonic decreasing in the interval (0,1) then the least value of the parameter m is

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)=logx, x in [1, e] , satisfies all the conditions of LMVT, then the value of c is

The function f(x) = 2x^(3) + 3x^(2) -12 x + 1 decreases in the interval

The least value of the function f(x) = 2 cos x + x in the closed interval [0,pi/2] is

The least value of the function f(x) = 2 cos x + x in the closed interval [0, (pi)/(2)] is:

The function f(x)=x^(2)+2x-5 is increasing in the interval

If f(x) = (x - 1)(x - 2)(x - 3)(x - 4)(x - 5) , then the value of f' (5) is equal to

Consider the function f(x)=tan^(-1){(3x-2)/(3+2x)}, AA x ge 0. If g(x) is the inverse function of f(x) , then the value of g'((pi)/(4)) is equal to