Question

If \(f(x)\) is an odd differentiable function defined on \((-\infty, \infty)\) such that \(f^{\prime}(3)=2\), then \(f^{\prime}(-3)\) equal to
(A) 0
(B) 1
(C) 2
(D) 4

Answer 1

Ans: (C)
Hint: Let \(f(x)=-f(-x)\)
$$
\begin{aligned}
&\Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=-\mathrm{f}^{\prime}(-\mathrm{x}) \cdot(-1)=\mathrm{f}^{\prime}(-\mathrm{x}) \\
&\therefore \mathrm{f}^{\prime}(-3)=\mathrm{f}^{\prime}(3)=2
\end{aligned}
$$

Answer 2

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