ISM_T11_C04_E - Section 4.4 Concavity and Curve Sketching...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 4.4 Concavity and Curve Sketching 231 21. When y x 5x , then y 5x 20x 5x (x 4) and œ± œ ± œ ± &% w% $$ y 20x 60x 20x (x 3). The curve rises on ww $ # # œ±œ ± ( ) and ( ), and falls on ( ). There is a local ±_ß! %ß_ !ß% maximum at x 0, and a local minimum at x 4. The œœ curve is concave down on ( 3) and concave up on ±_ß (3 ). At x 3 there is a point of inflection. ß_ œ 22. When y x 5 , then y 5 x(4) 5 œ ± ² ± ˆ‰ ˆ xx x ## # # %% $ w " 5 5 , and y 3 5 5 ± œ ± ± ˆ ˆ ˆ x5 x x 5 x # $# ww " 5 5 5 (x 4). The curve is rising ²± œ ± ± ˆ x # on ( ) and (10 ), and falling on ( 10). There is a ±_ß# local maximum at x 2 and a local minimum at x 10. The curve is concave down on ( ) and concave up on ±_ß% ( ). At x 4 there is a point of inflection. œ 23. When y x sin x, then y cos x and y sin x. œ² œ " ² ww w The curve rises on ( 2 ). At x 0 there is a local and œ 1 absolute minimum and at x 2 there is a local and absolute œ 1 maximum. The curve is concave down on ( ) and concave 1 up on ( ). At x there is a point of inflection. 11 1 ß# œ 24. When y x sin x, then y cos x and y sin x. œ " ± œ w The curve rises on ( 2 ). At x 0 there is a local and œ 1 absolute minimum and at x 2 there is a local and absolute œ 1 maximum. The curve is concave up on ( ) and concave 1 down on ( ). At x there is a point of inflection. 1 œ 25. When y x , then y x and y x . œ ± "Î& w ±%Î& ww ±*Î& " 52 5 4 The curve rises on ( ) and there are no extrema. ±_ß_ The curve is concave up on ( ) and concave down on ( ). At x 0 there is a point of inflection. !ß_ œ
Background image of page 1

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

View Full DocumentRight Arrow Icon
232 Chapter 4 Applications of Derivatives 26. When y x , then y x and y x . œœ œ ± $Î& w ±#Î& ww ±(Î& 36 52 5 The curve rises on ( ) and there are no extrema. ±_ß_ The curve is concave up on ( ) and concave down ±_ß! on ( ). At x 0 there is a point of inflection. !ß_ œ 27. When y x , then y x and y x . œ ± #Î& w ±$Î& ww ±)Î& 26 5 The curve is rising on (0 ) and falling on ( ). At ß_ x 0 there is a local and absolute minimum. There is œ no local or absolute maximum. The curve is concave down on ( ) and ( ). There are no points of inflection, but a cusp exists at x 0. œ 28. When y x , then y x and y x . œ ± %Î& w ±"Î& ww ±'Î& 44 5 The curve is rising on (0 ) and falling on ( ). At x 0 there is a local and absolute minimum. There is œ no local or absolute maximum. The curve is concave down on ( ) and ( ). There are no points of inflection, but a cusp exists at x 0. œ 29. When y 2x 3x , then y 2 2x and œ± #Î$ w ±"Î$ y x . The curve is rising on ( ) and ww ±%Î$ œ 2 3 ( ), and falling on ( ). There is a local maximum "ß_ !ß" at x 0 and a local minimum at x 1. The curve is concave up on ( ) and ( ). There are no points of inflection, but a cusp exists at x 0. œ 30. When y 5x 2x, then y 2x 2 2 x 1 œ ± œ ± #Î& w ±$Î& ±$Î& ˆ‰ and y x . The curve is rising on (0 1) and ww ±)Î& ß 6 5 falling on ( 0) and ( ). There is a local minimum ±_ß at x 0 and a local maximum at x 1. The curve is concave down on ( ) and ( ). There are no points of inflection, but a cusp exists at x 0. œ
Background image of page 2
Section 4.4 Concavity and Curve Sketching 233 31. When y x x x x , then œ± œ ± #Î$ #Î$ &Î$ ## ˆ‰ 55 y x x x (1 x) and w ±"Î$ #Î$ ±"Î$ œ ± 5 33 3 y x x x (1 2x).
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/20/2010 for the course MATHEMATIC 09991051 taught by Professor Dr.maenshadeed during the Fall '10 term at Norwegian Univ. of Science & Technology.

Page1 / 8

ISM_T11_C04_E - Section 4.4 Concavity and Curve Sketching...

This preview shows document pages 1 - 4. Sign up to view the full document.

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