Let f (x) be the function given by f(x)=3 x^ 5 -5 x^ 3 +21 x+3 x+4 x+5 . Then,

Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability

1. f (x) is increasing on R and \(f(x)=0\) has exactly one negative root
2. f (x) is decreasing on R and \(f(x)=0\) has exactly one positive root
3. f (x) is decreasing and \(f(x)=0\) has exactly one negative root
4. f (x) is increasing and \(f(x)=0\) has exactly one positive root.

Answer

(D) f (x) is increasing and f(x)=0 has exactly one positive root.

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