Exam 2 M112 2013 Fall

# Continue to next page 2 15 12 points find dydx in the

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15. (12 points) Find dy/dx in the following relations. (a) (6 points) cos( xy ) = 1 + sin y (b) (6 points) y = ( x 2 + 1) x Continue to Next Page 3
16. (7 points) Given the function f ( x ) = 1 x . (a) (2 points) Find the slope of the line which passes through the points (1 , f (1)) and (4 , f (4)). (b) (5 points) Find all numbers c such that f
( c ) will satisfy the conclusion of the mean value theorem on the interval [1 , 4]. Continue to Next Page 4

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17. (6 points) Use implicit di ff erentiation to derive the formula for d dx
sin 1 ( x )
. Your final answer should not include any trigonometric functions. 18. (8 points) Find the absolute maximum and absolute minimum values of the function f ( x ) = ( x 2 1) 3 on the interval [ 1 , 2]. Continue to Next Page 5
19. (8 points) A particle moves on a horizontal line so that its coordinate at time t is y = t 3 12 t + 3 , t 0. (a) (2 points) Find the velocity and acceleration functions. (b) (3 points) When is the particle moving to the right and when is it moving to the left? (c) (3 points) When is the particle speeding up? (Remember that speed is not the same as velocity.) Continue to Next Page 6

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20. (8 points) One car leaves an intersection and travels north at 30 miles per hour. Another car starts 10 miles west of this intersection and travels west at 35 miles per hour. At what rate is the distance between the two cars changing at the instant when the cars have traveled for 2 hours? END OF Part B 7
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