Final answer:
The given expression represents the slope of the line between two points on a curve.
Step-by-step explanation:
The given expression is s(a+h) + s(a). The quantity (a+h) represents a coordinate on the x-axis and s(a+h) represents the corresponding y-coordinate on the curve. The quantity a represents another coordinate on the x-axis and s(a) represents the corresponding y-coordinate on the curve. So, (a, s(a)) and (a+h, s(a+h)) are two points on the curve.
The slope of the line between these two points can be calculated using the formula:
slope = (change in y-coordinate) / (change in x-coordinate)
The change in y-coordinate is s(a+h) - s(a) and the change in x-coordinate is (a+h) - a, which simplifies to h. Therefore, the slope of the line is:
slope = (s(a+h) - s(a)) / h
So, the given expression represents the slope of the line between (a, s(a)) and (a+h, s(a+h)).