## Calculus (3rd Edition)

For $7\lt x\lt 9$
The slope of the tangent line at any point $x\gt7$ in the domain of the function is negative. As the derivative at a point is defined as the slope of the tangent line at that point, this implies that $f'(x)\lt0$ for $x\gt7$ where $x$ is in the domain of the function. In other words, $f'(x)\lt0$ for $7\lt x\lt9$ (The end-point 9 is excluded as no right-hand derivative exists at x=9).