Application of DerivativeHard
Question
The values of p for which the function f(x) = 
x5 - 3x + ln 5 decreases for all real x is
x5 - 3x + ln 5 decreases for all real x isOptions
A.(- ∞, ∞)
B.
∪ (1, ∞)
∪ (1, ∞)C.
∪ (2, ∞)
∪ (2, ∞)D.[1, ∞)
Solution
It is sufficient to solve for p, the condition f′(x) ≤ 0 ∀ x ∈ R
Case - I 1 - p < 0 p > 1
Inequality holds true.
Case - II 1 - p > 0 p < 1
Inequality holds if
- 1 ≤ 0
⇒ p ≥ - 4, p + 4 ≤ (1 - p)2
⇒ P ≥ - 4, p2 - 3p - 3 ≥ 0
⇒ - 4 ≤ p ≤
Hence p ∈
∪ (1, ∞)
Case - I 1 - p < 0 p > 1
Inequality holds true.
Case - II 1 - p > 0 p < 1
Inequality holds if
- 1 ≤ 0⇒ p ≥ - 4, p + 4 ≤ (1 - p)2
⇒ P ≥ - 4, p2 - 3p - 3 ≥ 0
⇒ - 4 ≤ p ≤
Hence p ∈
∪ (1, ∞)Create a free account to view solution
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