Question

If the function is not differentiable at the given value of x, tell whether the problem is a corner, cusp, vertical tangent, or a discontinuity. (attachment)

Answer 1

Take the derivative of the function.

Answer 2

@bloopman i got -1/(3x^(2/3))

Answer 3

Correct. Now, at x=0, that undefined?

Answer 4

yes?

Answer 5

Yeah. So if a line has an undefined slope, we can call it vertical. Therefore, it is a vertical tangent.

Answer 6

ok thanks!