Consider two statements S_1 and S_2. S_1: If | vedclass

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(C) Analysis of $S_1$: Let $f(x) = e^x$. Then $f'(x) = e^x > 0$. The function $g(x) = \frac{f(x)}{f'(x)} = \frac{e^x}{e^x} = 1$. Since $g(x) = 1$ is a

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$S_1$ is wrong and $S_2$ is right.

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(C) Analysis of $S_1$: Let $f(x) = e^x$. Then $f'(x) = e^x > 0$. The function $g(x) = \frac{f(x)}{f'(x)} = \frac{e^x}{e^x} = 1$. Since $g(x) = 1$ is a constant function,it is not strictly increasing. Thus,$S_1$ is false. Analysis of $S_2$: For $x \in (0, \frac{\pi}{2})$,$\frac{d}{dx}(\sin x) = \cos x > 0$ and $\frac{d}{dx}(	an x) = \sec^2 x > 0$. Since the derivatives are positive,both $\sin x$ and $	an x$ are strictly increasing in $(0, \frac{\pi}{2})$. Thus,$S_2$ is true. Therefore,$S_1$ is wrong and $S_2$ is right.

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