t belongs to rational numbers draw the graph of theta of t = t³-t²

Here is the graph of the function \( \theta(t) = t^3 - t^2 \), where \( t \) belongs to the set of rational numbers. The curve crosses the t-axis at \( t = 0 \) and \( t = 1 \), and features inflection points and a turning point.

Would you like further details or explanations about this graph?

Here are five related questions to consider:
1. How do the critical points of \( t^3 - t^2 \) affect the graph's shape?
2. What happens to the function as \( t \to \infty \) and \( t \to -\infty \)?
3. Can you determine the local minimum or maximum values of \( \theta(t) \)?
4. How would adding a constant term affect the graph of \( t^3 - t^2 \)?
5. How does the second derivative of the function relate to the concavity of the graph?

**Tip:** When analyzing polynomial graphs, identifying critical points and inflection points is key to understanding their shape and behavior.

t belongs to rational numbers draw the graph of theta of t = t³ - t²

Explore the graph of θ(t) = t³ - t², a cubic polynomial function, where t belongs to the rational numbers. Learn how to find the critical points, inflection points, and concavity using the first and second derivative tests. This problem is suitable for high school students studying polynomial functions in algebra.

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