https://file.aiquickdraw.com/mathbot/file/17260027374117rnin9zr.jpg

The image contains two similar mathematical expressions for the function \( h(x) \):

1. \( h(x) = 2x^3 - 3 \)
2. \( h(x) = 2x^3 - 3 \)

Both versions represent the same function, so we are working with the cubic function:

\[
h(x) = 2x^3 - 3
\]

Would you like to:

- Evaluate this function at a specific value of \(x\)?
- Find the derivative \(h'(x)\)?
- Find the integral of \(h(x)\)?
- Discuss its graph and behavior?
- Solve for when \( h(x) = 0 \)?

Let me know if you'd like more details on any aspect! Here are some possible next steps:

1. What is the value of \(h(x)\) when \(x = 2\)?
2. How do we find the turning points of \(h(x)\)?
3. What is the derivative of \(h(x)\)?
4. What is the behavior of the function as \(x\) approaches infinity or negative infinity?
5. How would you solve \(h(x) = 0\)?

**Tip:** Cubic functions like this often have one real root and two complex roots, depending on the discriminant of the cubic equation.

Explore the cubic function h(x) = 2x^3 - 3. Learn how to evaluate, differentiate, and analyze this polynomial function. Ideal for high school students, this problem touches on cubic function behavior, root finding, and calculus.

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