### Home > APCALC > Chapter 4 > Lesson 4.2.4 > Problem 4-90

4-90.

Earlier in this chapter, it was discovered that .

Why does the derivative of

not exist at ?What is the slope of the function at this point? Can you compute it?

Is

differentiable at ? Why or why not?Graph the function or evaluate the derivative at

. No, the tangent is still vertical (and in this case there is a cusp).

Is

differentiable at ? Why or why not?Simplify

.Explain why there is a point of inflection at

. What happens on either side of a point of inflection?What kind of change does a point of inflection signify?

Even though

, there is still a point of inflection because the graph changes from concave up to concave down at.