Final answer:
The function f(x) = 20 is a horizontal line, and therefore has a horizontal tangent for every point in the interval 0≤x≤20, indicating an infinite number of horizontal tangents.
Step-by-step explanation:
To determine the existence of horizontal tangents on the function f(x) = 20 within the interval 0≤x≤20, we need to analyze the slope of the function over this domain. Since the function is given as a constant, the graph of this function is a horizontal line. A horizontal line has a slope of 0, which means that every point on the line has a horizontal tangent.
In other words, for any value of x between 0 and 20, the function f(x) will not change and remains at the same y-value of 20. This indicates that there is a horizontal tangent at every point in the specified interval.
An important concept in this context is understanding that the slope of a tangent line to a curve at a given point represents the instantaneous rate of change of the function at that point. Since our function's rate of change is zero everywhere, it confirms the presence of horizontal tangents throughout the entire interval.