Question

the slope of the curve at point b
○ is equal to the slope at point a.
○ is less than the slope at point a.
○ is greater than the slope at point a.
○ cannot be compared with the slope at point a.
○ can be compared with the slope at point a, but more information is needed to determine if the slope is greater than, less than, or equal to the slope at point a.

Explanation:

To determine the slope of the curve at points \( A \) and \( B \), we analyze the steepness of the curve. The slope of a curve at a point is the slope of the tangent line at that point. For a concave - down curve (like the one shown, where the curve is increasing but at a decreasing rate), as we move from left to right (increasing the \( x \) - value, here "Hours of study (per week)"), the slope of the tangent line (the rate of change) decreases.

At point \( A \), the curve is steeper (the tangent line at \( A \) has a larger slope) compared to the tangent line at point \( B \). So the slope of the curve at point \( B \) is less than the slope at point \( A \).

Answer:

B. is less than the slope at point A.