For $7\lt x\lt 9$
Work Step by Step
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).