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ex1_6401

# ex1_6401 - P on a coordinate line is given by f t where t...

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Problem Sheet 1 for 6401 Due Monday 20 Oct 2008, at the Problem Class 1. Use the definition of derivative to find f 0 ( x ) (you are not allowed to use any rules for differentiating established in the course!): (a) f ( x ) = 17; (b) f ( x ) = - 6 x + π ; (c) f ( x ) = 15 - 3 x + 4 x 2 ; (d) f ( x ) = 1 x +3 ; (e) f ( x ) = 2 x + 3; (f) f ( x ) = 3 x ; (g) f ( x ) = 3 x 3 - 4 x . 2. Differentiate the following functions, using whichever rules for differentiating you find necessary: (a) f ( x ) = 3 x 4 x 2 +3 ; (b) f ( x ) = ( x + 1)( x 2 + 2)( x 3 + 3); (c) f ( x ) = r 1 + q 1 + p 1 + x ; (d) f ( x ) = 4 x 3 +sin( x + x ) e cos x - x 1 / 3 . 3. For f ( t ) = 3 t 2 + 2 t , the position of a point
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Unformatted text preview: P on a coordinate line is given by f ( t ), where t is measured in seconds and f ( t ) in centimeters. (a) Find the average velocity of P in the following time intervals: [1 , 1 . 2]; [1 , 1 . 1]; [1 , 1 . 01]; [1 , 1 . 001]. (b) Find the velocity of P at t = 1; (c) Determine the time intervals in which P moves in the positive direction; (d) Determine the time intervals in which P moves in the negative direction. 1...
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