ANOTHER PROBLEM FOR HANAH
on graph paper. Then without a calculator, sketch on the same set of axes.
Describe the graphs of
and at .
Use your graphing calculator to determine the slope of
at the vertex.
Though the derivative does not exist, some graphing calculators (inaccurately) say that the derivative is
at a cusp.
Calculators are not always accurate. Some graphing calculators incorrectly determine slopes at a vertex, as well as other cusps, because they use the symmetric difference quotient to calculate the slope of a tangent line.
, use , to calculate for and . What do you notice? What leads a calculator to give a false derivative of at ?