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

3-188.

ANOTHER PROBLEM FOR HANAH

Graph

on graph paper and*without your calculator*, sketch. What happens to

at the vertex? Use your graphing calculator to find the slope of

at the vertex. What happened?Though the derivative does not exist, some graphing calculators (inaccurately) say that the derivative is

at a cusp. Part of the reason most graphing calculators incorrectly determine slopes at the vertex of an absolute value graph, as well as other cusps, is because they use the symmetric difference quotient to calculate the slope of a tangent.

For, use to calculate

for,, and . What do you notice? What leads the calculator to falsely find a derivative of at ?