Active Calculus - Gvsu - Grand Valley State University

More documents

Recommendations

Info

34 2.1. ELEMENTARY DERIVATIVE RULESActivity 2.1.Use the three rules above to determine the derivative of each of the following functions. Foreach, state your answer using full and proper notation, labeling the derivative with its name.For example, if you are given a function h(z), you should write “h ′ (z) =” or “ dhdz=” as part ofyour response.(a) f(t) = π(b) g(z) = 7 z(c) h(w) = w 3/4(d) p(x) = 3 1/2(e) r(t) = ( √ 2) t(f)ddq [q−1 ](g) m(t) = 1 t 3⊳
2.1. ELEMENTARY DERIVATIVE RULES 35Activity 2.2.Use only the rules for constant, power, and exponential functions, together with the ConstantMultiple and Sum Rules, to compute the derivative of each function below with respect tothe given independent variable. Note well that we do not yet know any rules for how todifferentiate the product or quotient of functions. This means that you may have to do somealgebra first on the functions below before you can actually use existing rules to compute thedesired derivative formula. In each case, label the derivative you calculate with its name usingproper notation such as f ′ (x), h ′ (z), dr/dt, etc.(a) f(x) = x 5/3 − x 4 + 2 x(b) g(x) = 14e x + 3x 5 − x(c) h(z) = √ z + 1z 4 + 5 z(d) r(t) = √ 53 t 7 − πe t + e 4(e) s(y) = (y 2 + 1)(y 2 − 1)(f) q(x) = x3 − x + 2x(g) p(a) = 3a 4 − 2a 3 + 7a 2 − a + 12⊳
Page 1: Active CalculusMatt Boelkins, Lead
Page 5 and 6: Chapter 1Understanding the Derivati
Page 7 and 8: 1.1. HOW DO WE MEASURE VELOCITY? 3A
Page 9 and 10: 1.2. THE NOTION OF LIMIT 51.2 The n
Page 11 and 12: 1.2. THE NOTION OF LIMIT 7Activity
Page 13 and 14: 1.3. THE DERIVATIVE OF A FUNCTION A
Page 15 and 16: 1.3. THE DERIVATIVE OF A FUNCTION A
Page 17 and 18: 1.4. THE DERIVATIVE FUNCTION 131.4
Page 19 and 20: 1.4. THE DERIVATIVE FUNCTION 15rsxx
Page 21 and 22: 1.5. INTERPRETING THE DERIVATIVE AN
Page 23 and 24: 1.5. INTERPRETING THE DERIVATIVE AN
Page 25 and 26: 1.6. THE SECOND DERIVATIVE 21(a) In
Page 27 and 28: 1.6. THE SECOND DERIVATIVE 23• on
Page 29 and 30: 1.6. THE SECOND DERIVATIVE 25ffxxf
Page 31 and 32: 1.7. LIMITS, CONTINUITY, AND DIFFER
Page 33 and 34: 1.7. LIMITS, CONTINUITY, AND DIFFER
Page 35 and 36: 1.8. THE TANGENT LINE APPROXIMATION
Page 37: Chapter 2Computing Derivatives2.1 E
Page 41 and 42: 2.2. THE SINE AND COSINE FUNCTIONS
Page 43 and 44: 2.2. THE SINE AND COSINE FUNCTIONS
Page 45 and 46: 2.3. THE PRODUCT AND QUOTIENT RULES
Page 47 and 48: 2.3. THE PRODUCT AND QUOTIENT RULES
Page 49 and 50: 2.4. DERIVATIVES OF OTHER TRIGONOME
Page 51 and 52: 2.4. DERIVATIVES OF OTHER TRIGONOME
Page 53 and 54: 2.5. THE CHAIN RULE 492.5 The chain
Page 55 and 56: 2.5. THE CHAIN RULE 51Activity 2.14
Page 57 and 58: 2.6. DERIVATIVES OF INVERSE FUNCTIO
Page 59 and 60: 2.6. DERIVATIVES OF INVERSE FUNCTIO
Page 61 and 62: 2.7. DERIVATIVES OF FUNCTIONS GIVEN
Page 63 and 64: 2.7. DERIVATIVES OF FUNCTIONS GIVEN
Page 65 and 66: 2.8. USING DERIVATIVES TO EVALUATE
Page 67 and 68: 2.8. USING DERIVATIVES TO EVALUATE
Page 69 and 70: Chapter 3Using Derivatives3.1 Using
Page 71 and 72: 3.1. USING DERIVATIVES TO IDENTIFY
Page 73 and 74: 3.1. USING DERIVATIVES TO IDENTIFY
Page 75 and 76: 3.2. USING DERIVATIVES TO DESCRIBE
Page 77 and 78: 3.2. USING DERIVATIVES TO DESCRIBE
Page 79 and 80: 3.3. GLOBAL OPTIMIZATION 75Activity
Page 81 and 82: 3.3. GLOBAL OPTIMIZATION 77Activity
Page 83 and 84: 3.4. APPLIED OPTIMIZATION 79Activit
Page 85 and 86: 3.4. APPLIED OPTIMIZATION 81Activit
Page 87 and 88: 3.5. RELATED RATES 833.5 Related Ra
Page 89 and 90:
3.5. RELATED RATES 85Activity 3.15.
Page 91 and 92:
3.5. RELATED RATES 87Activity 3.17.
Page 93 and 94:
Chapter 4The Definite Integral4.1 D
Page 95 and 96:
4.1. DETERMINING DISTANCE TRAVELED
Page 97 and 98:
4.1. DETERMINING DISTANCE TRAVELED
Page 99 and 100:
4.2. RIEMANN SUMS 95⊲⊳
Page 101 and 102:
4.2. RIEMANN SUMS 97Activity 4.5.Su
Page 103 and 104:
4.3. THE DEFINITE INTEGRAL 994.3 Th
Page 105 and 106:
4.3. THE DEFINITE INTEGRAL 101Activ
Page 107 and 108:
4.3. THE DEFINITE INTEGRAL 103Activ
Page 109 and 110:
4.4. THE FUNDAMENTAL THEOREM OF CAL
Page 111:
4.4. THE FUNDAMENTAL THEOREM OF CAL
show all

Active Calculus - Gvsu - Grand Valley State University

Create successful ePaper yourself

Delete template?

Save as template?