MonotonicityHard
Question
The largest set of real values of x for which ln (1 + x) ≤ x is
Options
A.(-1, ∞)
B.(-1, 0) ∪ (0, ∞)
C.[0, ∞)
D.(0, ∞)
Solution
ln(1 + x) - x ≤ 0
Let f(x) = ln (1 + x) - x, [Domain is (-1, ∞)}
f′(x) =
⇒ f(x) ≤ f(0) ∀ x ∈ (-1, ∞) ⇒ (x) ≤ 0 ∀ x ∈ (1-, ∞).
Let f(x) = ln (1 + x) - x, [Domain is (-1, ∞)}
f′(x) =
⇒ f(x) ≤ f(0) ∀ x ∈ (-1, ∞) ⇒ (x) ≤ 0 ∀ x ∈ (1-, ∞).
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