Exams › JEE Main › Maths

For the function f(x) = (a² - 1)/(a² + 1)x³ - 3x + 5 to be decreasing for every real x, the admissible values of the parameter a are

1. (1, ∞)
2. (-∞, -1)
3. [-1, 1]
4. None of these

Correct answer: [-1, 1]

Solution

The function is decreasing when its derivative is less than or equal to zero for all x. By analyzing the derivative, we find that the condition for it to be non-positive is satisfied when a is within the range [-1, 1], ensuring that the cubic term does not dominate and cause the function to increase.

Related JEE Main Maths questions

• Evaluate the limit as x approaches 0: ((1+tan x)/(1+sin x))^(csc x).
• Evaluate the limit as x approaches 0 of sin([x−3]) divided by [x−3], where [.] denotes the greatest integer function.
• Evaluate the limit as x approaches 0: (sin(x⁴) − x⁴ cos(x⁴) + x²⁰) / (x⁴(e^(2x⁴) − 1 − 2x⁴)).
• Evaluate the limit lim_(n→∞)(n³-8)/(n³+8). What is its value?
• If lim_(x→∞) (1+(λ)/(x)+(μ)/(x²))^(2x)=e², which of the following values of λ and μ is correct?
• Consider the following statements: Statement 1: If lim_(x→α)(sin(f(x)))/(x-α), where f(x)=ax²+bx+c, exists as a finite nonzero number, then lim_(x→α)(1/f(x)-1)/(1/f(x)+1) does not exist. Statement 2: The limit lim_(x→α)(sin(f(x)))/(x-α) can be finite only in the indeterminate form 0/0.

⚔️ Practice JEE Main Maths free + battle 1v1 →