LIST I

LIST II

 A. strictly increasing

 I. either increasing or decreasing on a given interval 

 B. differentiable real function 

 II. $x^2+3 x+5, x \in R$ 

 C. a monotonic function 

 III. if $x_1<x_2 \Rightarrow f\left(x_1\right)>f\left(x_2\right)$ for all $x_1, x_2 \in(a, b)$ 

 D. strictly decreasing 

 IV. if $x_1<x_2 \Rightarrow f\left(x_1\right)<f\left(x_2\right)$ for all $x_1, x_2 \in[a, b]$