Monotonicity Questions

Function f (x) = x2(x - 2)2 is -

The function f (x) = tan x - x

The function f, defined by f (x) = (x + 2)e-x is -

Function f (x) = x3 + 6x2 + (9 +2k) x + 1 is increasing function if

The function f(x) = cos x - 2px is monotonically decreasing for

The value of ′a′ for which the function f(x) = sin x - cosx - ax + b decreases for all real value of x, is -

Let f(x) be a quadratic expression which is positive for all real values of x. If g(x) = f(x) + f′(x) + f″x), then for any real x -

f(x) = dx then f is -

Let f(x) = Which of the following properties does f have on the interval (0, 6) ?I. ln f(x) exist; II. f is continuous III. f is monotonic...

The length of largest continuous interval in which function f (x) = 4x - tan2x is monotonic, is -

The largest set of real values of x for which ln (1 + x) ≤ x is

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

Number of solution of the equation 3tan x + x3= 2 in is

Rolle′s theorem in the indicated intervals will not be valid for which of the following function -

Consider the function for x = [-2, 3], f(x) = if x ≠ 1, then

If the function f(x) = 2x2 + 5 satisfies LMVT at x = 2 on the closed interval [1, a] then the value of ′a′ is equal to -

Consider the function f(x) = 8x2 - 7x + 5 on the interval [-6, 6]. The value of c that satisfies the conclusion of the mean value theorem, is -

Let f be a function which is continuous and differentiable for all real x. If f(2) = - 4 and f′(x) ≥ 6 for all x ∈ [2, 4] then

If f(x) = x3 + 7x - 1 then f(x) has a zero between x = 0 and x = 1. The theorem which best describes this, is -

Consider f(x) = l 1 - x l , 1 ≤ x ≤ 2 and g(x) = f(x) + b sin π/2 x, 1 ≤ x ≤ 2 then which of the following is correct ?