📝 Graphs With Vertical Tangents And Cusps

Q1. For the function \(f(x)=\sqrt[3]{x}\), at which x‑value does the graph have a vertical tangent?

💡 Difficulty: easy | ✅ Correct: B

Q2. Where does the graph of \(f(x)=\frac{1}{\sqrt{x}}\) exhibit a vertical tangent?

💡 Difficulty: medium | ✅ Correct: A

Q3. For the function \(p(x)=x^{1/3}\sin\frac{1}{x}\) (with \(p(0)=0\)), determine the nature of the point at \(x=0\).

💡 Difficulty: hard | ✅ Correct: C