1. Stating the problem: Find $q$ given by the formula $q = \sqrt[3]{2r} - r^2$ where $r$ is a variable. 2. Understand the expression: The first term is the cube root of $2r$, written as $\sqrt[3]{2r} = (2r)^{1/3}$. 3. The second term is $r^2$, which is $r$ squared. 4. So the function is: $$q = (2r)^{1/3} - r^2$$ 5. We can evaluate or analyze $q$ for various values of $r$, depending on the context. 6. For example, to find $q$ at $r=1$: $$q = (2 \cdot 1)^{1/3} - 1^2 = 2^{1/3} - 1 \approx 1.26 - 1 = 0.26$$ 7. At $r=0$, we get: $$q = (2 \cdot 0)^{1/3} - 0 = 0 - 0 = 0$$ 8. This function represents the difference between the cube root growth of $2r$ and the quadratic growth of $r^2$. Final answer: $$q = \sqrt[3]{2r} - r^2$$