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Unformatted text preview: f ( t )] iv. Since part iii. can be rewritten as f ( t ) = 1 60 { 15 2[ f ( t )15] 2 } , we see that the maximum of f ( t ) occurs at t = 15 m. Find the time t at which this occurs. v. Use the info in i.iv. to sketch the graph of y = f ( t ). BONUS PROBLEM. Prove the following xed point result. If f : [0 , 1] [0 , 1] is continuous then it must have a xed point. (i. e. c [0 , 1] s.t. f ( c ) = c ) Hint: apply IVT to g : [0 , 1] [0 , 1] ,g ( x ) = f ( x )x ....
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 Spring '08
 Oancea
 Calculus

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