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determine whether​ Rolle's Theorem applies to the following function on the given interval. If​ so, find...

determine whether​ Rolle's Theorem applies to the following function on the given interval. If​ so, find the​ point(s) that are guaranteed to exist by​ Rolle's Theorem.​g(x)=x^3 + 7 x ^2 - 5 x - 75​; ​[- 5​,3​]

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