An auxanometer (Gr. auxain, "to grow" + metron, "measure") is an apparatus for measuring increase or rate of growth in plants.
In case of an arc-auxanometer (see picture), there is a wire fixed with the plant apex on one end and a dead-weight on the other.
An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima.
For example, for the curve plotted given, the red point is an inflection point.