AP EAMCET · Maths · Functions
If \(f: R \rightarrow R\) is an even function having derivatives of all orders, then an odd function among the following is
- A \(f^{\prime \prime}\)
- B \(f^{\prime \prime \prime}\)
- C \(f^{\prime}+f^{\prime \prime}\)
- D \(f^{\prime \prime}+f^{\prime \prime \prime}\)
Answer & Solution
Correct Answer
(B) \(f^{\prime \prime \prime}\)
Step-by-step Solution
Detailed explanation
Since, \(f\) is an even function. Let \[ \begin{aligned} f(x) & =\cos x \\ f^{\prime}(x) & =\sin x \\ f^{\prime \prime}(x) & =-\cos x \\ f^{\prime \prime \prime}(x) & =\sin x \end{aligned} \] Since, \(\sin x\) is an odd function. \(\therefore\) In \(f^{\prime \prime \prime}\) it…
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