SOLUTION: Calculus Question Use the Intermediate Value Theorem and Rolle's Theorem to determine that {{{ f(x)=x^7+4x^5+3x+5 }}} has exactly one real root between -1 and 0.

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Question 1142316: Calculus Question
Use the Intermediate Value Theorem and Rolle's Theorem to determine that +f%28x%29=x%5E7%2B4x%5E5%2B3x%2B5+ has exactly one real root between -1 and 0.
Answer by solver91311(24713) About Me  (Show Source):
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If a function is continuous on the closed interval and has values and at each end of the domain interval, then the function takes on any value in the interval at some point in the domain interval.

All polynomial functions with real coefficients are everywhere continuous.



is a polynomial function with real coefficients and is therefore everywhere continuous and is therefore continuous on the interval .





Therefore has any value in the interval for some

therefore


John

My calculator said it, I believe it, that settles it