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The lecturer is saying

Initially the gradient is positive and fairly constant, but for it drops to zero at the peak, it then becomes negative for a period before returning to zero.

Cambridge gives this explanation about fairly

more than average, but less than very

which seems not to be the case here.

enter image description here

assume the initial part is the time frame between the starting point, shown above, and somewhere shown below

enter image description here

Technically, in the initial part, the gradient (the slop of the orange line) is not a constant. but it could be viewed as a constant, when compared to the one shown below.

enter image description here

If the meaning "more than average" is taken, where is the average? So, it seems that "fairly" mean "relatively" in this case, is my understanding right?

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    It isn't talking about the average gradient of the graph, it means fairly relative to the gradient at the rest of the points in the graph. A better definition would be - more than a little; to some degree Cambridge Dictionary – Gamora Aug 14 '19 at 9:54
  • A typical thing a mathematician might say is "for small angles, tan(x) is fairly close to sin(x)." The lecturer means it in this mathematical sense: "approximately", "quite", without being specific. You can indeed see it's pretty close: he just means "straight-ish", and is contrasted to the part where the curve visibly changes direction. (He also doesn't mean the dictionary sense using "average", nor any mathematical meaning of average.) – jonathanjo Aug 14 '19 at 13:19
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'fairly' = 'somewhat'

It's an indeterminate positive indicating that something is positively true - but it does not quantize how much it is true.

Other Synonyms = 'a little', 'slightly'

Fairly is stronger than 'a little', and stronger than 'slightly' but a weaker comparison than 'frequently'

Truth is a binary concept in logic - but has degrees in language. My guess at the following, going from weakest to strongest 'slightly' 'a little' 'somewhat' 'fairly' 'commonly' 'frequently' 'almost always' 'solely' / 'always' '

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