Question

Draw a graph on the paper to match the description. g(x) has a negative derivative over (−[infinity],−7) and (3,7) and a positive derivative over (−7,3) and (7,[infinity]).

Answer 1

A sketch of a graph with the given conditions can be seen in the image below.

Which function can be this?

A negative derivative means that the function goes down in that interval, and a positive derivative means that it goes up.

So let's take piecewise function:

Decreases in (-∞, -7)

Increases in (-7, 3)

Decreases in (3, 7)

Increases in (7, ∞)

The graph that does this can be seen in the image below: