Explanation Given: If the function f is continuous and has no zeros on [ a , b ] , then either f ( x ) > 0 for all x in [ a , b ] or f ( x ) < 0 for all x in [ a , b ] . Formula used: Intermediate value theorem: If the function f is continuous on the closed interval [ a , b ] , f ( a ) ≠ f ( b ) and k is any number between f ( a ) and f ( b ) , then there is at least one number c in [ a , b ] such that f ( c ) = k . Proof: Suppose there are two numbers x 1 and x 2 in [ a , b ] , such that both are opposite in sign. That is, if f ( x 1 ) > 0 , then f ( x 2 ) < 0 or if f ( x 1 ) < 0 , then f ( x 2 ) > 0

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ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 1.4, Problem 117E

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To prove: If the function f is continuous and has no zeros on [a,b], then either f(x)>0 for all x in [a,b] or f(x)<0 for all x in [a,b].

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Chapter 1.4, Problem 116E

Chapter 1.4, Problem 118E

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To prove: If the function f is continuous and has no zeros on [ a , b ] , then either f ( x ) > 0 for all x in [ a , b ] or f ( x ) < 0 for all x in [ a , b ] .

Solution Summary: The author proves that the function f is continuous and has no zeros on left[a,bright].

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To prove: If the function f is continuous and has no zeros on [a,b], then either f(x)>0 for all x in [a,b] or f(x)<0 for all x in [a,b].

Want to see the full answer?

Chapter 1 Solutions

To prove: If the function f is continuous and has no zeros on [ a , b ] , then either f ( x ) &gt; 0 for all x in [ a , b ] or f ( x ) &lt; 0 for all x in [ a , b ] .

Solution Summary: The author proves that the function f is continuous and has no zeros on left[a,bright].

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To prove: If the function f is continuous and has no zeros on [a,b], then either f(x)>0 for all x in [a,b] or f(x)<0 for all x in [a,b].

Want to see the full answer?

Chapter 1 Solutions

To prove: If the function f is continuous and has no zeros on [ a , b ] , then either f ( x ) > 0 for all x in [ a , b ] or f ( x ) < 0 for all x in [ a , b ] .