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(D) An increasing function $f(x)$ on $[a, b]$ does not necessarily have to be continuous or differentiable.$1$. Since $f(x)$ is increasing,for any $x_

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Equation $f(x) = c, c \in (f(a), f(b))$ has at most one solution.

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(D) An increasing function $f(x)$ on $[a, b]$ does not necessarily have to be continuous or differentiable.$1$. Since $f(x)$ is increasing,for any $x_1 $2$. The range of $f(x)$ is a subset of $[f(a), f(b)]$,but it is not necessarily equal to $[f(a), f(b)]$ if the function is discontinuous.$3$. $f'(x)$ may not exist at all points,so $f'(x) \geq 0$ is not always true.$4$. For any $c \in (f(a), f(b))$,if $f(x) = c$ had two distinct solutions $x_1 Therefore,option $D$ is the most appropriate choice.

If a function $f(x)$ is increasing in an interval $x \in [a, b]$,then which of the following will always be correct?

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