MonotonicityHard

Question

Equation - 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 x
Domain 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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