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Let f (t) be the temperature at time t where you live and suppose that at time t − 3 you feel uncomfortably hot. How do you feel about the given data in each case?

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Patrina Schowalter
Patrina SchowalterLv2
22 May 2020

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2. (20 pts) An object begins moving along a vertical line at time t = Os and stops at time t = 6 s. Its height above the ground at time t is given by h(t) in the provided graph, where h is measured in meters. Use the graph to answer the following questions. on 0 (a) Compute the average velocity of the object on the time interval [0,6). Show your work. N 1 2 3 4 5 6 (b) Circle the choice that best describes the shape of the graph on the time interval (5,6). i. increasing and concave up ii. increasing and concave down iii. decreasing and concave up iv. decreasing and concave down (c) At what time is the object farthest away from the ground? What is the velocity at that time? time= velocity= (d) The maximum velocity attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2 s iii. 3s iv. 4s v. 5s (e) Estimate the value of the maximum velocity attained. The value is an integer. (f) Let v(t) be the velocity at time t. Circle the greatest value amongst the following choices. i. v(2.5) ii. (2.6) ii. v(2.7) iv. v(2.8) V. (2.9) (8) List the time interval(s) on which the velocity is increasing. Use integer endpoints. (h) The maximum speed attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2s iii. 35 iv. 4s v. 5s

(a) If we start from latitude and proceed in a westerly direction, we can let denote the temperature at the point x at any given time. Assuming that T is a continuous function of x, show that at any fixed time there are at least two diametrically opposite points on the equator that have exactly the same temperature.

(b) Does the result in part (a) hold for points lying on any circle on the earth’s surface?

(c) Does the result in part (a) hold for barometric pressure and for altitude above sea level?

A manufacturing company owns a major piece of equipment that depreciates at the (continuous) rate, where t is the time measured in months since its last overhaul. Because a fixed cost A is incurred each time the machine is overhauled, the company wants to determine the optimal time T (in months) between the overhauls.

  1. Explain whyrepresents the loss in value of the machine over the period of time t since the last overhaul.

  2. Letbe given by,

What does C represents and why would the company want to minimize C?

  1. Show that C has a minimum value at the numberswhere.

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