KCET · Maths · Application of Derivatives
If \(f(x)\) is an even function and \(f^{\prime}(x)\) exists, then \(\mathrm{f}^{\prime}(\mathrm{e})+\mathrm{f}^{\prime}(-\mathrm{e})\) is
- A \(>0\)
- B 0
- C \(\geq 0\)
- D \( < 0\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
Since, \(f(x)\) is an even function, therefore \(f^{\prime}(x)\) is an odd function.
\[
f^{\prime}(-e)=-f^{\prime}(e)
\]
\(\therefore \quad \mathrm{f}^{\prime}(\mathrm{e})+\mathrm{f}^{\prime}(-\mathrm{e})=0\)
\[
f^{\prime}(-e)=-f^{\prime}(e)
\]
\(\therefore \quad \mathrm{f}^{\prime}(\mathrm{e})+\mathrm{f}^{\prime}(-\mathrm{e})=0\)
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