An earth satellite in an elliptical orbit travels slowest when it is

The satellite travels slowest when it is at the maximum distance from the Earth.

We can verify this in two ways:

1) By using Kepler's second law: "A line segment joining a a satellite with the Earth covers equal areas during equal intervals of time". This means that the larger is the distance of the satellite from Earth, the slower it goes.

2) by looking at the forces acting on the satellite. There is only one force acting on it: the gravitational attraction exerted by Earth, and this force is the centripetal force that keeps the satellite in circular (elliptical, actually) motion. So we can write:

where on the left we wrote the formula of the gravitational force, while on the right the centripetal force. G is the gravitational constant, M the Earth's mass, m the satellite's mass, v its velocity and r the distance of the satellite from the center of Earth.
Simplifying, we get

which is the speed of the satellite when it is at a distance r from Earth: the larger r, the smaller the speed v.

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