Question

Mathematics

The figure shows the Graph of

inflection sfows the graph of a function . The zero and extrema for are labeled, and the point of Of the of the graph of is labeled. Let A, B, C, D. and represent the -coordinates at those points. Of the following, on which interval is decreasing and the graph of concave down?

(A) the interval from to

(B) the interval from to

(C) the interval from to

(D) the interval from to

inflection sfows the graph of a function

(A) the interval from

(B) the interval from

(C) the interval from

(D) the interval from

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Best Answer

(A) the interval from to .

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 is decreasing on the interval from to , because the slope is negative in that region.

To determine whether is concave down on this interval, we can look at the shape of the graph. Since has an inflection point at , the concavity of the graph must change at that point. Specifically, is concave up on the interval from to , and concave down on the interval from to . Therefore, is concave down on the interval from to as well.

Since is decreasing and concave down on the interval from to , the correct answer is (A) the interval from to .

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

To determine whether

Since