1. Given that functions $h(x)$ and $g(x)$ are both increasing functions defined on the interval $(0,+\infty)$, and let the function $f(x)=$ $h(x) g(x)$. Then the function $f(x)$ on the interval $(0,+\infty)$ ( ).
(A) must be an increasing function
(B) may be an increasing function, or may be a decreasing function, one of the two must be true
(C) may be an increasing function, or may be a decreasing function, or may be a constant function, one of the three must be true
(D) none of the above is correct
- 1.D.

Example: $h(x)=-\frac{1}{x}, g(x)=\ln x$, which is an increasing function on $(0,+\infty)$. But $f(x)=h(x) g(x)=-\frac{\ln x}{x}$, its derivative is $f^{\prime}(x)=\frac{\ln x-1}{x^{2}}$.
$$
\begin{array}{l}
\text { On }(0, \mathrm{e}) \text {, } f^{\prime}(x)0 .
\end{array}
$$