Exams › JEE Advanced › Maths

Which of the following statements is/are correct regarding monotonicity of functions?

1. x + sin x is an increasing function
2. sec x is neither increasing nor decreasing function
3. x + sin x is a decreasing function
4. sec x is an increasing function

Correct answer: x + sin x is an increasing function

Solution

d/dx(x + sin x) = 1 + cos x which is always >= 0 (and = 0 only at isolated points x = (2k+1)*pi), so the function is non-decreasing (increasing in the broader sense used at this level). sec x has derivative sec x * tan x which changes sign across its domain, so sec x is neither globally increasing nor globally decreasing.

Related JEE Advanced Maths questions

• What is the proportion between the height of the cone with the largest possible volume that can fit inside a sphere and the sphere's diameter?
• Identify the point on the curve 9y² = x³ where the normal to the curve intersects the coordinate axes at equal distances.
• The normal to the parametric curve defined by x = a(cos θ + sin θ) and y = a(sin θ − cos θ) at any given value of θ:
• How many critical points exist for the function y = f(x) within the interval x ∈ [0, 2], if the function satisfies d²y/dx² = 6x - 4 and has a local minimum value of 5 at x = 1?
• What is the absolute minimum value of y = f(x) on the interval x ∈ [0, 2], given that f(x) satisfies the equation d²y/dx² = 6x - 4 and has a local minimum value of 5 at x = 1?
• The function f(x) = 2 |x| + |x+2| - ||x+2|-2| - |2|x|| has a local minimum or a local maximum at x =

⚔️ Practice JEE Advanced Maths free + battle 1v1 →