ISM_T11_C04_D - 224 (c) Chapter 4 Applications of...

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

View Full Document Right Arrow Icon
224 Chapter 4 Applications of Derivatives (c) 35. (a) h(x) 2x 4x h (x) x 4x 4 (x 2) a critical point at x 2 h [ and œ ± ² Ê œ ± ² œ ± Ê œ Ê œ ²²² ³ ²²² ! # x 3 $ #w # # w h(0) 0 no local maximum, a local minimum is 0 at x 0 œÊ œ (b) no absolute maximum; absolute minimum is 0 at x 0 œ (c) 36. (a) k(x) x 3x 3x 1 k (x) 3x 6x 3 3(x 1) a critical point at x 1 œ² ²²Ê œ ²²œ ² Ê œ ± $# w # # k ] and k( 1) 0, k(0) 1 a local maximum is 1 at x 0, no local minimum Ê œ ²²² ³ ²²² ± œ œ Ê œ ±" ! w (b) absolute maximum is 1 at x 0; no absolute minimum œ (c) 37. (a) f(x) 2 sin f (x) cos , f (x) 0 cos a critical point at x œ± Ê œ Ê œ xx x x 2 3 ## # # # # ww "" ˆ‰ 1 f [ ] and f(0) 0, f 3, f(2 ) local maxima are 0 at x 0 and Ê œ ±±± ³ ²²² œ œ ± œ Ê œ !# $ w 1 1 11 1 È 2 33 at x 2 , a local minimum is 3 at x œ 1 2 È (b) The graph of f rises when f 0, falls when f 0, ´µ and has a local minimum value at the point where f w changes from negative to positive.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Section 4.3 Monotonic Functions and the First Derivative Test 225 38. (a) f(x) 2 cos x cos x f (x) 2 sin x 2 cos x sin x 2(sin x)(1 cos x) critical points at œ± ± Ê œ ² œ ² Ê #w x , 0, f [ ] and f( ) 1, f(0) 3, f( ) 1 a local maximum is 1 at Ê œ ±±±³²²² ± œ œ Ê ± ! 11 1 1 w x , a local minimum is 3 at x 0 œ„ ± œ 1 (b) The graph of f rises when f 0, falls when f 0, ww ´µ and has local extreme values where f 0. The w œ function f has a local minimum value at x 0, where œ the values of f change from negative to positive. w 39. (a) f(x) csc x 2 cot x f (x) 2(csc x)( csc x)(cot x) 2 csc x 2 csc x (cot x 1) a critical Êœ ± ± ± œ ± ± Ê # # ab a b point at x f ( ) and f 0 no local maximum, a local minimum is 0 at x œ Ê œ ±±± ³ ²²² œ Ê œ ! Î% 1 44 4 w 1 1 ˆ‰ (b) The graph of f rises when f 0, falls when f 0, and has a local minimum value at the point where f 0 and the values of f change from negative to œ positive. The graph of f steepens as f (x) . w Ä„_ 40. (a) f(x) sec x 2 tan x f (x) 2(sec x)(sec x)(tan x) 2 sec x 2 sec x (tan x 1) a critical point ± œ ± Ê # # at x f ( ) and f 0 no local maximum, a local minimum is 0 at x œ Ê œ ±±± ³ ²²² œ Ê œ ±Î # Î # Î% 1 4 w 1 (b) The graph of f rises when f 0, falls when f 0, and has a local minimum value where f 0 and the w œ values of f change from negative to positive. w 41. h( ) 3 cos h ( ) sin h [ ] , ( ) and ( 3) a local maximum is 3 at 0, )) 1 ) 1 œ Ê œ ± Ê œ ±±± !ß$ # ß± Ê œ !# ## # 3 a local minimum is 3 at 2 ±œ )1 42. h( ) 5 sin h ( ) cos h [ ] , ( 0) and ( 5) a local maximum is 5 at , a local 1 ) 1 1 œ Ê œ Ê œ ²²² ß Ê œ ! # 5 minimum is 0 at 0 ) œ
Background image of page 2
226 Chapter 4 Applications of Derivatives 43. (a) (b) (c) (d) 44. (a) (b) (c) (d) 45. (a) (b) 46. (a) (b) 47. f(x) x 3x 2 f (x) 3x 3 3(x 1)(x 1) f rising for x c since œ ± ² Ê œ ± œ ± ² Ê œ ²²² ³ ±±± ³ ²²² Ê œ œ # ±" " $w # w f (x) 0 for x c 2. w ´œ œ 48. f(x) ax bx c a x x c a x x c a x
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 / 7

ISM_T11_C04_D - 224 (c) Chapter 4 Applications of...

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