WBJEE · Maths · Application of Derivatives
Let \(f(x)=x^2+x \sin x-\cos x\). Then
- A \(f(x)=0\) has at least one real root
- B \(f(x)=0\) has no real root
- C \(f(x)=0\) has at least one positive root
- D \(f(x)=0\) has at least one negative root
Answer & Solution
Correct Answer
(D) \(f(x)=0\) has at least one negative root
Step-by-step Solution
Detailed explanation
\(f^{\prime}(x)=2 x+x \cos x+\sin x+\sin x=2(x+\sin x)+x \cos x\) \(\Rightarrow f^{\prime}(x) > 0 \quad \forall x > 0, \quad f^{\prime}(x)
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