Straight Across. A line that goes straight across (Horizontal) has a Gradient of zero.

What if the gradient is zero?

It's like being at the top of a mountain: any direction you move is downhill. A zero gradient tells you to stay put – you are at the max of the function, and can't do better.

Is the gradient 0 at a minimum?

Just before a minimum point the gradient is negative, at the minimum the gradient is zero and just after the minimum point it is positive.