If y = f(x) is an odd differentiable function defined on $(-\infty, \infty)$ such that f'(3) = -2, then f'(-3) equals
Answer & explanation
Correct answer: option 3
Since f(x) is an odd differentiable function defined on R. Therefore,
$f(-x)=-f(x)$ for all $x \in R$
Differentiating both sides w.r.t. x, we get
$-f'(-x)=-f'(x)$ for all $x \in R$
$\Rightarrow f'(-x)=f'(x)$ for all $x \in R$
$\Rightarrow f'(-3)=f'(3)=-2$
ALITER We know that the derivative of a differentiable odd function is an even function. Therefore, f'(x) is an even function. Hence,
$f'(-3)=f'(3)=-2$