questions about cusps and tangent lines in Derivatives

these questions i have answeared uncorrectly and don't understand why i'm wrong, anyway here are the questions:

Determine whether f has :

(a)a vertical tangent line at (0,0)

(b)a cusp at (0,0)

(1)f(x) = x ^ (1/3)

**Correct Answear:** (a)yes (b) no

**My Answear:** (a)no (b)no

(2)f(x) = x ^ (2/5)

**Correct Answear:** (a)yes (b)yes

**My Answear:** (a)no (b)no

(3)f(x) = 5x ^ (3/2)

**Correct Answear:** (a)no (b)no

**My Answear:** (a)yes (b)no

if there is a cusp at a point then the right hand limit = infinity and the left hand limit = infinity with opposite signs at that point ?

and a vrtical tangent line means the dericative of f at this point = infinity?