Difference between revisions of "009A Sample Final A, Problem 10"
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(Created page with "<span style="font-size:135%"><font face=Times Roman>10. Consider the function <math style="vertical-align: -15%;">f(x)=2x^{3}+4x+\sqrt{2}.</math> <br> (a)...") |
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| − | |< | + | |<u>'''The Intermediate Value Theorem</u>.''' ''If f''(''x'')'' is a continuous function on the interval ''[''a,b'']'', and if f''(''a'')'' ≤ f''(''b'')'', then for any y such that f''(''a'')'' ≤ y ≤ f''(''b'')'', then there exists a c ∈ ''[''a,b'']'' such that f''(''c'')'' = y.'' |
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Revision as of 20:26, 23 March 2015
10. Consider the function
(a) Use the Intermediate Value Theorem to show that has at
least one zero.
(b) Use Rolle's Theorem to show that has exactly one zero.
| Foundations |
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| The Intermediate Value Theorem. If f(x) is a continuous function on the interval [a,b], and if f(a) ≤ f(b), then for any y such that f(a) ≤ y ≤ f(b), then there exists a c ∈ [a,b] such that f(c) = y. |