MonotonicityHard
Question
Equation 
- 3x + sin x = 0 has -
- 3x + sin x = 0 has -Options
A.no real root
B.two real and distinct roots
C.exactly one negative root
D.exactly one root between -1 and 1
Solution
f(x) =
- 3x sin xDomain of ′f′ is (-∞, - 1) υ (-1, ∞)
f(x) = - 3
+ cos x.⇒ f′(x) < 0 ⇒ f is decreasing
f(x) → ∞ 
f(x) → - ∞
f(x) → - ∞ 
f(x) → ∞ ⇒ f(x) = 0 has exactly two roots.
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