Let f and g be two differentiable functions on R such that f^′(x)>0 and g^′(x)<0, for all x ∈ R. Then for all x:

Let $\displaystyle f$ and $\displaystyle g$ be two differentiable functions on $\displaystyle \mathbf{R}$ such that $\displaystyle f^{\prime}(x)>0$ and $\displaystyle g^{\prime}(x)<0$, for all $\displaystyle x \in \mathbf{R}$. Then for all $\displaystyle x$ :