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hw10-26 - Math 170-007 Homework 10/26 Fall 2010 Section 6.5...

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Math 170-007 Homework 10/26 Fall 2010 Section 6.5: Mean Value Theorem. In all of these problems, use the MVT f ( b ) - f ( a ) b - a = f ( c ) to compute or estimate f ( b ) from the given data. You may assume that f is suitably continuous and differentiable. 1. f (2) = 10. f ( x ) = - 3 for all x in [2 , 7]. Find f (7). 2. f (2) = 10. f ( x ) = - 3 for all x in [2 , 7]. Find f (5). 3. f (2) = 10. f ( x ) = - 3 for all x . Find f (20). 4. f (2) = 10. f ( x ) = - 3 for all x . Find f ( x ). 5. f ( - 3) = - 4. f ( x ) 5 for all x in [ - 3 , 3]. Estimate f (3). 6. f (3) = - 4. 5 f ( x ) 6 for all x in [ - 3 , 3]. Estimate f ( - 3). 7. f (3) = - 4. 5 f ( x ) 6 for all x in [ - 3 , 3]. Estimate f (0). 8. f (3) = - 4. f ( x ) 5 for all x in [ - 3 , 3]. Estimate f ( x ) if x is in [ - 3 , 3]. 9. f ( a ) = 10. f ( x ) < 0 for all x in [ a, b ]. Estimate f ( b ). 10. f ( a ) = k . f ( x ) < 0 for all x in [ a, b ]. Estimate f ( x ). if x is in ( a, b ). 11. f ( a ) = k . f ( x ) = 0 always. Compute f ( x ) for any x . Section 5.1 and 5.2: Min/Max and Inc/Dec. In each of these problems, do the following: Locate all critical points. Analyze the first derivative. Sketch the function. This can be a bad sketch, but it must have exact x -coordinates for
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