COMEDK · Maths · 24. Functions
If \(f(x)\) is an even function and \(f^{\prime}(x)\) exists, then \(f^{\prime}(e)+f^{\prime}(-e)\) is
- A \(>0\)
- B 0
- C \(\geq 0\)
- D \( < 0\)
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
We have, \(f(x)\) is an even function. \[ \begin{array}{ll} \therefore & f(-x)=f(x) \\ \Rightarrow & f^{\prime}(-x)(-1)=f^{\prime}(x) \\ \Rightarrow & f^{\prime}(x)+f^{\prime}(-x)=0 \\ \Rightarrow & f^{\prime}(e)+f^{\prime}(-e)=0 \end{array} \]
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