Graph the curves in Exercises 37–46. a. Where do the graphs appear to have vertical tan...

Graph the curves in Exercises 37–46.

a. Where do the graphs appear to have vertical tangents?

b. Confirm your findings in part (a) with limit calculations. But before you do, read the introduction to Exercises 35 and 36.

We say that a continuous curve y = f(x) has a vertical tangent at the point where x = x₀ if

For example, y = x^1/3 has a vertical tangent at x = 0 (see accompanying figure):

However, y = x^2/3 has no vertical tangent at x = 0 (see next figure):

does not exist, because the limit is from the right and from the left.