Clicker Question 1

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# Clicker Question 1 - PowerPoint PPT Presentation

Clicker Question 1. What is the derivative of f ( x ) = arctan(5 x )? A. arcsec 2 (5 x ) B. 5 arcsec 2 (5 x ) C. 5 / (1 + 5 x 2 ) D. 5 / (1 + 25 x 2 ) E. 1 / (1 + 25 x 2 ). Clicker Question 2.

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## Clicker Question 1

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Clicker Question 1
• What is the derivative of f (x ) = arctan(5x )?
• A. arcsec 2 (5x )
• B. 5 arcsec 2 (5x )
• C. 5 / (1 + 5x2)
• D. 5 / (1 + 25x2)
• E. 1 / (1 + 25x2)
Clicker Question 2
• What is the slope of the tangent line to the curve y = x arcsin(x) at the point (1, /2)?
• A. 0
• B. 1
• C. /2
• D. ½
• E. undefined
Applications of the Derivative to the Sciences (2/7/11)
• Sciences (both natural and social) have numerous applications of the derivative. Some examples are:
• Population growth or decay (Biology etc.)
• Input: time
• Output: the size of some population
• The derivative is the rate of growth or decay of that population with respect to time.
Applications: Economics
• Marginal Cost
• Input: Some production level
• Output: The cost of producing at that level
• The derivative is the rate of change of cost with respect to production level, called the marginal cost.
• Likewise marginal profit
Applications: Physics
• There are many such applications. We look at just one easy one:
• Velocity:
• Input: time
• Output: position of a moving object
• The derivative is the rate of change of position with respect to time, i.e., velocity.
• The second derivative is the rate at which the velocity is changing. What’s that called?
Example of Velocity & Acceleration
• Suppose the position of a car on a highway (in miles from the start) is given by s(t) = 50t + 3 sin(t ) where t is in hours.
• What is its position after 5 hours?
• What is its velocity after 5 hours?
• What is its acceleration after 5 hours?
• (Include units in all answers!)
Assignment for Wednesday
• Read pages 221 through 223 of Section 3.7 up to Example 2.
• Do Exercises 1 a.b.c.g., 3 a.b.c.g., 7 and 9 on pages 230-231.