112S20Hwk2 Solution.pdf - MAT 112 Spring 2020 Homework 2...

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MAT 112 Homework 2 Name: Solution Spring 2020 Monday, February 3 Section 3.1 13. For the function 𝑓𝑓 ( 𝑥𝑥 ) = 𝑥𝑥 2 + 𝑥𝑥 and a = 1, use Equation 3.4 to find the slope of the tangent line, 𝑚𝑚 𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑓𝑓′ ( 𝑎𝑎 ) , and find the equation of the tangent line to 𝑓𝑓 ( 𝑥𝑥 ) at x = 1.
23. For the function 𝑓𝑓 ( 𝑥𝑥 ) = 𝑥𝑥 2 + 9 𝑥𝑥 and a = 2, find 𝑓𝑓 ( 𝑎𝑎 ) using Equation 3.3.
47. Two vehicles start out traveling side by side along a straight road. Their position functions, shown in the graph, are given by 𝑠𝑠 = 𝑓𝑓 ( 𝑡𝑡 ) and 𝑠𝑠 = 𝑔𝑔 ( 𝑡𝑡 ) , where s is measured in feet and t is measured in seconds. a. Which vehicle has traveled farther at t = 2 seconds?
b. What is the approximate velocity of each vehicle at t = 3 seconds?
c. Which vehicle is traveling faster at t = 4 seconds?
d. What is true about the positions of the vehicles at t = 4 seconds?
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Section 3.2 55. For 𝑓𝑓 ( 𝑥𝑥 ) = 2 3 𝑥𝑥 , use the definition of the derivative to find 𝑓𝑓′ ( 𝑥𝑥 ) .
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