A curve increases when the y value of the curve increases as the x value of the curve increases.

The gradient at a point is the gradient of the tangent at that point, and this gradient can be found using:

It is positive when y2 > y1 and x2 > x1, or when y1 > y2 and x1 > x2.

The moment you have the y and x coordinates of a point greater than the y and x coordinates of another point, you have an increasing 'curve' (it can be a line).

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