AP EAMCET · Maths · Application of Derivatives
At \(\mathrm{x}=0, f(x)=\cos x-1+\frac{x^2}{2}-\frac{x^3}{3}\)
- A has a minimum value
- B has a maximum value
- C has no extremum value
- D is not defined
Answer & Solution
Correct Answer
(C) has no extremum value
Step-by-step Solution
Detailed explanation
We are given that \(f(x)=\cos x-1+\frac{x^2}{2}-\frac{x^3}{3}\) \(\begin{aligned} & \Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=-\sin \mathrm{x}+\mathrm{x}-\mathrm{x}^2 \\ & \Rightarrow \mathrm{f}^{\prime \prime}(\mathrm{x})=-\cos \mathrm{x}+1-2 \mathrm{x}\end{aligned}\) At…
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