Question

5. Explain (concisely) along with a labelled diagram the following terms: a) local or relative extrema b) absolute extrema c) turning points d) inflection point e) critical points

Answer 1

Critical Points - Points on the graph of a function where the derivative is zero or the derivative does not exist.

Local extrema -  A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.

Absolute Extrema - An absolute extremum (or global extremum) of a function in a given interval is the point at which a maximum or minimum value of the function is obtained.

Turning point - A turning point is a point at which the derivative changes sign. A turning point may be either a relative maximum or a relative minimum (also known as local minimum and maximum). If the function is differentiable, then a turning point is a stationary point; however not all stationary points are turning points.

Inflection Point - 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.