﻿ The set of all values of a for which the function                     decreases for all real x is : Kaysons Education

# The Set Of All Values Of A For Which The Function                     Decreases For All Real x is

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## Question

### Solution

Correct option is

Differentiating, we get

For f (x) to be decreasing for all x, we must have f ‘(x) < 0 for all x.

This is possible only if

This inequality is always true if a > 1, i.e., a ∈ (1, ∞). Moreover, we must have a ≥ – 4 for  to be real. Therefore, we have

[∴  we consider only a < 1]

⇒ a + 4 ≤ 1 + a2 – 2a ⇒ 0 ≤ a2 – 3a – 3

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