Applications of...

 The interval in which the function x³  increases less rapidly than 6x²  + 15x + 5 is

The function   is monotonically decreasing in

 If y = (a + 2) x³  – 3ax²  + 9ax – 1 decreases monotonically   x ∈R then `a 'lies in the interval

The true set of real values of x for which the function, f(x) = x  l n x – x + 1 is positive is

 The set of all x for which  l n (1 + x) ≤x is equal to

 The curve y = f(x) which satisfies the condition f '(x) >0 and f "(x) <0 for all real x, is

If the point (1, 3) serves as the point of inflection of the curve y = ax³  + bx²  then the value of `a 'and `b 'are

The function f(x) = x³  – 6x²  + ax + b satisfy the conditions of Rolle 's theorem in [1, 3]. The value of a and b are

 If f(x) =  ; g(x) =   for a >1, a ¹1 and x ÎR, where {*} &[*] denote the fractional part and integral part functions respectively, then which of the following statements holds good for the function h(x), where (l n a) h(x) = (l n f(x) +l n g(x)).

Let f(x) = (x – 4) (x – 5) (x – 6) (x – 7) then,

Given that f is a real valued differentiable function such that f(x) f '(x) <0 for all real x, it follows that