I've done the first part, but I'm stuck on the second paragraph of the question. Maybe I'm being stupid, I don't even understand exactly what is meant by, 'the level curve'.
I also don't quite understand the whole concept of directional derivative. When it says, 'the gradient in the direction making an angle A with the x-axis, how should I think of this? what does the gradient mean in this context?
because when its just a simple curve/line on an xy axis, I know what the 'gradient' means, it is literally how much 'y' changes per unit x along that curve/line. But when I'm told about a 'gradient in a direction', I'm confused.