TS EAMCET · Maths · Continuity and Differentiability
If \(f: R \rightarrow R\) is an even function which is twice differentiable on \(R\) and \(f^{\prime \prime}(\pi)=1\), then \(f^{\prime \prime}(-\pi)\) is equal to
- A -1
- B 0
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
Let the even function be \(f(x)=\cos x\) On differentiating w.r.t. \(x\), we get \(f^{\prime}(x)=-\sin x\) Again differentiating w.r.t. \(x\), we get \(f^{\prime \prime}(x)=-\cos x\) at \(x=\pi\) \(f^{\prime \prime}(\pi)=-\cos \pi=1\) \(\therefore\) Our assumption is true. at…
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