MAT135H1 Lecture Notes - Lecture 22: Marginal Cost

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30 Oct 2018

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MAT135H1 Lecture Notes - Lecture 21: Logarithmic Differentiation

MAT135H1 Lecture Notes - Lecture 22: Marginal Cost

MAT135H1 Lecture 23: MAT135 - Lecture 23 - Exponential Growth and Decay

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Mat135 - lecture 22 - rates of change. Read sections 3. 6 and 3. 7 from the textbook. Recall the idea of interpreting derivatives as rates of change. Let = f ( ) be a given quantity. The average rate of change of with respect to. Over the interval [ 1 , 2 ] is given by. = f ( 2 ) - f ( 1 ) / 2 - 1 y x . The instantaneous rate of change of with respect to is given by dy dx lim. This interpretation of the derivative can be applied in all kinds of disciplines and scenarios; it"s what makes the derivative important. Describe the motion of an object given its position s ( t ) at all time t. Let v ( t ) be the velocity of the object at time t and let a ( t ) be the acceleration of the object at time t , then:

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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

MAT135H1 Lecture Notes - Lecture 22: Marginal Cost

MAT135H1 Lecture Notes - Lecture 21: Logarithmic Differentiation

MAT135H1 Lecture Notes - Lecture 22: Marginal Cost

MAT135H1 Lecture 23: MAT135 - Lecture 23 - Exponential Growth and Decay

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