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# hw2answers - Villarreal Natalie Homework 2 Due Sep 4 2007...

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Villarreal, Natalie – Homework 2 – Due: Sep 4 2007, 3:00 am – Inst: Louiza Fouli 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Yes, Homework 1 is due AFTER Homework 2. 001 (part 1 of 1) 10 points A car first slows down, but then speeds up. Sketch a graph of the position of the car as a function of time. 1. time position 2. time position 3. time position 4. time position 5. time position 6. time position correct Explanation: When the position of the car is plotted against time, the slope of the graph indicates the speed of the car, the greater the slope, the greater the speed, and the car is stationary when the slope is zero. Thus of the graphs, only

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Villarreal, Natalie – Homework 2 – Due: Sep 4 2007, 3:00 am – Inst: Louiza Fouli 2 time position has the given properties. Keywords: graphical interpretation speed, position v. time graph 002 (part 1 of 1) 10 points The point P (1 , 8 5 ) lies on the graph of the function f defined by f ( x ) = 8 x 3 + 2 x . By calculating the slope of the secant line PQ for the successive points Q ( x, f ( x )) with x = 1 . 1 , x = 1 . 01 , x = 1 . 001 , x = 1 . 0001 , and x = 0 . 9 , x = 0 . 99 , x = 0 . 999 , x = 0 . 9999 , estimate (to 3 decimal places) the slope of the tangent line to the graph of f at P . Correct answer: 0 . 96 . Explanation: The slope of the secant line PQ for general points P ( a, f ( a )) and Q ( b, f ( b )) on the graph of f is given by rise run = f ( b ) - f ( a ) b - a .
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