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Question

# Prove that$f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 4 x$has no root c satisfying c > 0. Hint: Note that x = 0 is a root and apply Rolle's Theorem.

Solution

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$\text{\underline{Theorem 4 Rolle's Theorem:}}$\ Assume that f is continuous on [a, b] and differentiable on (a,b). if $f(a)=f(b)$ then there exists a number c between a and b such that $f'(c)=0$

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