### Home > CALC > Chapter 4 > Lesson 4.2.4 > Problem 4-93

4-93.

In Chapter 4, 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).

What about

? Simplify

.Explain why there is a point of inflection at

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

Even though

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