This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: mora-boellstorff (erm823) 4.9 Arledge (55875) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points If the graph of f is which one of the following contains only graphs of anti-derivatives of f ? 1. 2. 3. 4. 5. 6. cor- rect Explanation: If F 1 and F 2 are anti-derivatives of f then F 1 ( x ) F 2 ( x ) = constant independently of x ; this means that for any two anti-derivatives of f the graph of one is just a vertical translation of the graph of the other. But no horizontal translation of the graph of an anti-derivative of f will be mora-boellstorff (erm823) 4.9 Arledge (55875) 2 the graph of an anti-derivative of f , nor can a horizontal and vertical translation be the graph of an anti-derivative. This rules out two sets of graphs. Now in each of the the remaining four fig- ures the dotted and dashed graphs consist of vertical translations of the graph whose line- style is a continuous line. To decide which of these figures consists of anti-derivatives of f , therefore, we have to look more carefully at the actual graphs. But calculus ensures that (i) an anti-derivative of f will have a local extremum at the x-intercepts of f . This eliminates two more figures since they contains graphs whose local extrema occur at points other than the x-intercepts of f . (ii) An anti-derivative of f is increasing on interval where the graph of f lies above the x-axis, and decreasing where the graph of f lies below the x-axis. Consequently, of the two remaining figures only consists entirely of graphs of anti-derivatives of f . keywords: antiderivative, graphical, graph, geometric interpretation 002 10.0 points A modern jet fighter aircraft needs to be travelling at 180 yards/sec down the runway in order to take off. It is known that the jet can accelerate from 0 to 180 yards/sec in 10 seconds (assume constant acceleration). Determine the shortest length the runway can be if the plane starts from rest at one end and has to take off at least 200 yards before the runway ends?...
View Full Document
- Fall '10