Test: Monotonicity - JEE MCQ

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

 The set of all x for which ln (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 ¹ 1 and x Î R, where {*} & [*] denote the fractional part and integral part functions respectively, then which of the following statements holds good for the function h(x), where (ln a) h(x) = (ln f(x) +ln 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

If f(x) = ; g(x) = where 0 < x < 1, then

 f : R → R be a differentiable function x ∈ R. If tangent drawn to the curve at any point x ∈ (a, b) always lie below the curve, then

A value of C for which the conclusion of Mean Value Theorem holds for the function f(x) = log_e x on the interval [1, 3] is

The function f(x) = x(x + 3) e^–x/2 satisfies all the conditions of Rolle’s theorem in [–3, 0]. The value of c which verifies Rolle’s theorem, is

 x³ – 3x² – 9x + 20 is

 f(x) = x² - x sin x is

The number of values of `c' of Lagrange's mean value theorem for the function,

f(x) = (x – 1) (x – 2) (x – 3), x ∈ (0, 4) is

If f(x) and g(x) are differentiable in [0, 1] such that f(0) = 2, g(0) = 0, f(1) = 6, g(1) = 2, then Rolle's theorem is applicable for which of the following

Equation 3x² + 4ax + b = 0 has at least one root in (0, 1) if

Function for which LMVT is applicable but Rolle's theorem is not

 LMVT is not applicable for which of the following ?