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Eastern Imports
How to show function crosses between intveral (1, infinity)?
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<blockquote data-quote="TylerQ" data-source="post: 1661739" data-attributes="member: 535264"><p>Hey, i have a question that asks</p><p></p><p>Show that the following function has exactly one zero in the given interval</p><p></p><p>f(x) = -(1/5)x^3 - (7/x^2) + (20/x), given interval (1, infinity)</p><p></p><p>i got f ' (x) already which is </p><p></p><p>(-3x^5-100x+70)/5x^3</p><p></p><p>and i know that it will cross 0 at 3 (by plugging f ' (x) into graph).. but how do i show that mathematically?</p><p></p><p></p><p>thanks!</p></blockquote><p></p>
[QUOTE="TylerQ, post: 1661739, member: 535264"] Hey, i have a question that asks Show that the following function has exactly one zero in the given interval f(x) = -(1/5)x^3 - (7/x^2) + (20/x), given interval (1, infinity) i got f ' (x) already which is (-3x^5-100x+70)/5x^3 and i know that it will cross 0 at 3 (by plugging f ' (x) into graph).. but how do i show that mathematically? thanks! [/QUOTE]
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