y^3 = 4x^2

y^3 = 4x^2

If x is doubled, by what factor does y increase?

$\begin{array}{lcll} \boxed{~ \begin{array}{lcll} y^3 &=& 4\cdot x^2 \end{array} ~} \end{array}\\ \begin{array}{rcll} \\ (y\cdot f)^3 &=& 4\cdot (2x)^2 \\ y^3\cdot f^3 &=& 4\cdot 4 \cdot x^2 \qquad & | \qquad 4 \cdot x^2 = y^3\\ y^3\cdot f^3 &=& 4\cdot y^3\\ f^3 &=& 4\\ \mathbf{f} &\mathbf{=}& \mathbf{\sqrt[3]{4}}\\ \end{array}\\$

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