# ISM_T11_C03_B - Section 3.3 The Derivative as a Rate of...

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

Section 3.3 The Derivative as a Rate of Change 139 27. (a) y 6 1 6 1 1 œ± ² Ê œ ± ˆ‰ Š‹ tt t t 1 6 144 dt 12 dy # # # (b) The largest value of is 0 m/h when t 12 and the fluid level is falling the slowest at that time. The dy dt œ smallest value of is 1 m/h, when t 0, and the fluid level is falling the fastest at that time. dy dt ±œ (c) In this situation, 0 the graph of y is dy dt ŸÊ always decreasing. As increases in value, dy dt the slope of the graph of y increases from 1 ± to 0 over the interval 0 t 12. ŸŸ 28. (a) V r 4 r 4 (2) 16 ft /ft œÊ œ Ê œ œ 4d V d V 3d r d r 11 1 1 \$# # \$ ¸ r=2 (b) When r 2, 16 so that when r changes by 1 unit, we expect V to change by approximately 16 . œœ dV dr Therefore when r changes by 0.2 units V changes by approximately (16 )(0.2) 3.2 10.05 ft . Note œ¸ \$ that V(2.2) V(2) 11.09 ft . ±¸ \$ 29. 200 km/hr 55 m/sec m/sec, and D t V t. Thus V t t 25 sec. When œ Ê œ œ Ê œ Ê œ 5 500 10 20 500 20 500 99 9 9 9 9 9 # t 25, D (25) m œ 10 6250 # 30. s v t 16t v v 32t; v 0 t ; 1900 v t 16t so that t 1900 Ê œ ± œ Ê œ œ ± !! ! # # # vv 32 32 3 64 ! ! ## v (64)(1900) 80 19 ft/sec and, finally, 238 mph. Êœ œ ¸ ! È È 80 19 ft sec 1 min 1 hr 5280 ft 60 sec 60 min 1 mi È †† 31. (a) v 0 when t 6.25 sec (b) v 0 when 0 t 6.25 body moves up; v 0 when 6.25 t 12.5 body moves down ³ Ÿ ´Ê ´ ´ (c) body changes direction at t 6.25 sec œ (d) body speeds up on (6.25 12.5] and slows down on [0 6.25) ßß (e) The body is moving fastest at the endpoints t 0 and t 12.5 when it is traveling 200 ft/sec. It's moving slowest at t 6.25 when the speed is 0. œ (f) When t 6.25 the body is s 625 m from the origin and farthest away.

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

View Full Document
140 Chapter 3 Differentiation 32. (a) v 0 when t sec œœ 3 # (b) v 0 when 0 t 1.5 body moves down; v 0 when 1.5 t 5 body moves up ±Ÿ ± Ê ² ± Ÿ Ê (c) body changes direction at t sec œ 3 # (d) body speeds up on and slows down on ‘‰ ˆ ± 33 ## ß& (e) body is moving fastest at t 5 when the speed v(5) 7 units/sec; it is moving slowest at œ kk t when the speed is 0 œ 3 # (f) When t 5 the body is s 12 units from the origin and farthest away. 33. (a) v 0 when t sec 61 5 3 È (b) v 0 when t body moves left; v 0 when 0 t or t 4 ±± ± Ê ² Ÿ ± ± Ÿ 5 5 561 5 3 3 ±² ± ² ÈÈ È È body moves right Ê (c) body changes direction at t sec œ 5 3 È (d) body speeds up on and slows down on 0 . Š‹ Š’ 5 5 5 5 ß# ³ ß% ß ³ #ß (e) The body is moving fastest at t 0 and t 4 when it is moving 7 units/sec and slowest at t sec œ 5 3 È (f) When t the body is at position s 6.303 units and farthest from the origin. œ¸ ´ 5 3 ² È
Section 3.4 Derivatives of Trigonometric Functions 141 34. (a) v 0 when t œœ 61 5 3 È (b) v 0 when 0 t or t 4 body is moving left; v 0 when ±Ÿ ± ± Ÿ Ê ² 561 5 33 ±² ÈÈ t body is moving right 5 5 ±± Ê (c) body changes direction at t sec œ 5 3 È (d) body speeds up on and slows down on Š‹ Š’ 5 5 5 5 ß# ³ ß% ³ #ß (e) The body is moving fastest at 7 units/sec when t 0 and t 4; it is moving slowest and stationary at t œ 5 3 È (f) When t the position is s 10.303 units and the body is farthest from the origin.

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

View Full Document
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 / 21

ISM_T11_C03_B - Section 3.3 The Derivative as a Rate of...

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

View Full Document
Ask a homework question - tutors are online