Identifying Graph with Specific Derivatives
The problem in the image is asking to identify the graph of a function g(x) that has a positive derivative over the interval (-∞, -4) and a negative derivative over the interval (-4, ∞).
A positive derivative means that the function is increasing on that interval, and a negative derivative means the function is decreasing on that interval.
Let's examine each option:
A. This graph shows a function that is decreasing (negative derivative) over the interval (-∞, -4) and increasing (positive derivative) over the interval (-4, ∞). This is the opposite of what we're looking for.
B. This graph shows a function that is increasing (positive derivative) over the interval (-∞, -4) and decreasing (negative derivative) over the interval (-4, ∞). This matches the description given.
C. This graph shows a function that is increasing over both intervals, which does not match the given criteria of a positive derivative only over (-∞, -4) and a negative derivative over (-4, ∞).
Therefore, the correct graph that matches the description given is option B.
