Final answer:
The horizontal tangent line to a curve at the point (1/5, 4/5), which requires understanding derivatives and their role in determining the slope of tangents in calculus.
Step-by-step explanation:
A horizontal tangent line to a curve at a given point, which in this case is (1/5, 4/5). The concept of a horizontal tangent line implies that the slope of the tangent is zero at that particular point on the curve. When calculating the slope of a tangent to a curve, we're dealing with the derivative of the function at a specific point, which gives us the rate of change (slope) of the function at that point.
For a horizontal tangent line, the derivative is equal to zero. Understanding how to find the slope of a curve at a given point and how to write the equation of the tangent line is crucial in calculus, which is often part of the high school mathematics curriculum.