HW4solution-Part2 - Math 16A, Fall 2007 Professor Stankova...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 16A, Fall 2007 Professor Stankova Félice Lê Homework 4 Solutions – Part 2 Section 1.8 1.8#4 a) The average rate of change is given by 5 2 7 1 2 12 2 ) 2 ( 3 3 12 2 ) 3 ( 3 2 3 ) 2 ( ) 3 ( = - = - + - - + = - - f f . b) The instantaneous rate of change when 2 = t is given by ) 2 ( f . We use the Sum Rule to differentiate each term of ) ( t f separately. - + + = t dt d dt d t dt d t f 12 2 3 ) ( Then we apply the Power Rule to each term. 2 1 12 3 12 0 3 12 2 3 ) ( - - + = - + = - + + = t t dt d t dt d dt d t dt d t f . Then 6 4 12 3 ) 2 ( 12 3 ) 2 ( 2 = + = + = - f . 1.8#6 Note that the t -value in the graph represents the number of years since January 1, 1950. Therefore, t =10 represents January 1, 1910, t =20 represents January 1, 1920, and so forth. a) We are looking at the points (20, 150) and (60, 300) on the curve. The average rate of change is 4 15 20 60 150 300 20 60 ) 20 ( ) 60 ( = - - = - - f f . b) The speed at which the mean farm size was rising on January 1, 1950, is equivalent to the instantaneous rate of change at t = 50, or ) 50 ( f . This in turn is equivalent to the slope of the tangent line to the graph at t = 50. This tangent line is shown on the graph. We can choose any two 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
points on the line to calculate its slope; using the points (40, 150) and (80, 400), ) 50 ( 4 25 40 80 150 400 f x y m = = - - = = . c) We can see that at t = 60, the graph is steeper than at t = 80. In other words, the slope of the graph (and of the tangent line) is greater at t = 60. Therefore, we conclude that the mean farm size was rising faster on January 1, 1960, than on January 1, 1980. 1.8#10 The rate at which the liquid is flowing into the vat is given by
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/03/2008 for the course MATH 16A taught by Professor Stankova during the Spring '07 term at University of California, Berkeley.

Page1 / 6

HW4solution-Part2 - Math 16A, Fall 2007 Professor Stankova...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online