Final answer:
The exact values of c where f ' changes from positive to negative cannot be determined without the specific function or its derivative. The points where the slope changes from uphill to downhill are sought, which in physical terms relate to the highest points of a motion on a velocity-time graph.
Step-by-step explanation:
To find the value(s) of c where f ' changes from positive to negative, we need to analyze the behavior of the derivative of a function, which indicates the slope of the function at any given point.
The slope of the function corresponds to the instantaneous rate of change, which in physics can relate to instantaneous velocity. At the points where f ' changes from positive to negative, the function's slope changes from an uphill slope to a downhill slope, which typically occurs at a peak or local maximum of the function.
If we had the actual function or its derivative, we would set f ' equal to zero and solve for c to find the critical points. Then, by using the First Derivative Test, we could determine where f ' changes signs by plugging in values around our critical points into f '.
In physics, these points of change in velocity might correspond to the highest or lowest points of a path or motion described by the velocity-time graph, often where acceleration changes.
Since we do not have a specific function provided in the question, the exact values of c cannot be determined without further information.