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Mathematics
The figure shows the Graph of f f
inflection sfows the graph of a function f f. The zero and extrema for f f are labeled, and the point of Of the of the graph of f f is labeled. Let A, B, C, D. and E E represent the x x-coordinates at those points. Of the following, on which interval is f f decreasing and the graph of f f concave down?
(A) the interval from A A to B B
(B) the interval from B B to C C
(C) the interval from C C to D D
(D) the interval from D D to E E
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(A) the interval from A A to B B.
A decreasing function has a negative slope, and a concave down function has a decreasing rate of increase. We can use this information to determine which interval satisfies both conditions.
From the graph, we can see that f f is decreasing on the interval from A A to B B, because the slope is negative in that region.
To determine whether f f is concave down on this interval, we can look at the shape of the graph. Since f f has an inflection point at C C, the concavity of the graph must change at that point. Specifically, f f is concave up on the interval from A A to C C, and concave down on the interval from C C to E E. Therefore, f f is concave down on the interval from C C to D D as well.
Since f f is decreasing and concave down on the interval from A A to B B, the correct answer is (A) the interval from A A to B B.
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