WBJEE · Maths · Functions
\(F(x)=\cos x-1+\frac{x^2}{2!}, x \in \mathbb{R}\). Then \(f(x)\) is
- A decreasing function
- B increasing function
- C neither increasing nor decreasing
- D constant \(\forall x\gt0\)
Answer & Solution
Correct Answer
(C) neither increasing nor decreasing
Step-by-step Solution
Detailed explanation
Hint : \(f(x)=\cos x-1+\frac{x^2}{2!}, x \in R \Rightarrow f^{\prime}(x)=-\sin x-0+\frac{2 x}{2!}=x-\sin x\) \(\begin{array}{lll} f^{\prime}(x)\gt0 & \forall x\gt0 & \because x\gt\sin x \\ f^{\prime}(x) \lt 0 & \forall x \lt 0 & \because x \lt \sin x \end{array}\)…
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