Math

The range of the function.

\(h(x) = 5x^2 + 20x + 33/x^2\\ h'(x)=10x+20-\dfrac{66x}{x^4}=0\\ 10x^4+20x^3-66=0\\ x\in\{-2.4492, 1.2645\}\)

The function has minima at \(M_1(-2.4492, -13.4897)\) and \(M_2(1.2645, 53.9232)\).

At x = 0, the function value grows to infinity.

\(\color{blue}So\ R\in \{-13.4897\le \mathbb R< infinity\}\)

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