Final answer:
The question seeks to identify the interval where a graph is concave down. Option (b) (0,1) is the correct answer because the graph is described as concave downward in that interval according to the provided information.
Step-by-step explanation:
The question is asking us to determine on which interval the graph of a function is concave down. Concavity of a curve relates to the direction that the curve bows relative to the x-axis. When a graph is concave down, it means that it opens downward like a frown or the inside of an umbrella. Concave down sections of a graph are where the second derivative is negative, indicating that the slope of the tangent lines is decreasing as you move from left to right.
Given the descriptions provided for different parts of a curve or graph, we can examine which section has the characteristic shape of a concave down curve. From the options given:
- (a) Describes a graph that begins with a nonzero y-intercept with a downward slope that levels off at zero, which implies concavity changing from down to up.
- (b) Describes a graph where part A is concave downward, and this matches our requirement for concavity.
- (c) Describes a graph that is concave upward initially and then concave downward at the end.
- (d) Describes a situation with multiple intervals of different slopes and concavities.
Based on this information and focusing on the description of a curve that is concave down, option (b) clearly matches our criteria. Thus, the correct answer is (b) (0,1) where the graph is described as having a curve that is concave downward in the first 15 minutes.