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The image contains the following problems involving curve sketching:

8. Sketch the curve \( y = x^3(6x^2 - 15x + 10) \).
9. Sketch the curve \( a^4y = x(x^2 - 15a^2)^2 \).
10. Sketch the curve \( y = x(x - 2)^{\frac{2}{3}} \).

Would you like help with solving one of these problems step-by-step, or would you like to discuss specific concepts or methods related to curve sketching?

Let me know if you want to dive deeper into one of these problems. Also, here are some related questions to consider:

1. How do you determine the critical points for a given function?
2. What role does the second derivative play in curve sketching?
3. How do you identify inflection points on a graph?
4. What does the behavior of a function at infinity tell you about the sketch?
5. How do you determine the intervals of concavity for a function?

**Tip**: Always check for symmetry (even or odd function) before starting your sketch, as it can simplify the process significantly.

Sketch the curve y = x^3(6x^2 - 15x + 10). Sketch the curve a^4y = x(x^2 - 15a^2)^2. Sketch the curve y = x(x - 2)^(2/3).

Learn how to sketch curves for functions like y = x^3(6x^2 - 15x + 10), a^4y = x(x^2 - 15a^2)^2, and y = x(x - 2)^(2/3) with step-by-step solutions. Key concepts include critical points, inflection points, and behavior at infinity. Suitable for undergraduate calculus students.

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