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Find the Lipschitz constant. $$g(t,u)=10t^{2}\exp(-3u^3)$$ where $|(t)|\leq2$ and $|u|\leq1$

The function $g(t,u)$ is continuous over the Domain. So it satisfies the Lipschitz condtion. For Lipschitz constant: $$\frac{\partial{g}}{\partial t}=-120t^2u^2\exp(-3u^3)$$ It will have the maximum value at $u=-1$ and $t=2$ . so $$-120t^2u^2\exp(-3u^3)=-120\exp(1)$$ Is it correct?

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