Get the "furthest point away" along a B-Spline in a segment

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Given a B-Spline define by n + 1 control points and degree p, and a specific "t" value segment between knots e.g. 0.6 <= t <+ 0.7, I need to find the point at which the B-Spline "bulges" the furthest away from the straight line between the knots i.e. the furthest distance perpendicular distance from the straight line that interpolates the two knots to any point on that segment.

How can I accomplish this?