Bonus $[5$ pts$]$ You are given that a function $f$ is continuous on the interval $(2,7)$ and that $f(x)0$ for all $x$ in $(2,7).$ Prove that $f(x)>0$ for all $x$ in $(2,7)$ or that $f(x)<mn>0</mn>$ for all $x$ in $(2,7).$ Cite all theorems used. $[$This was a fundamental idea in determining where a function, derivative, or second derivative is positive or negative.$]$