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\text { (a) What is the maximizer of } g:[-4,4] \rightarrow \mathbb{R} \text { given by } g(x)=\frac{1}{2} x^{3}-\frac{1}{2} x^{2}-6 x+\frac{27}{2} \text { ? } \text { What is } \int_{0}^{1} g(x) d x \text { for } g \text { defined above? }

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