### Home > APCALC > Chapter 3 > Lesson 3.4.4 > Problem 3-188

3-188.

ANOTHER PROBLEM FOR HANAH

Graph

on graph paper. Then without a calculator, sketchDescribe the graphs of

andat.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.

For, use^{ }, to calculate forand. What do you notice? What leads a calculator to give a false derivative of ^{ }at?