Test 2

Question 1

Chain rule

Answer 1

Question 2

Derivative of Power functions:

Answer 2

Question 3

Derivative of:

Answer 3

Question 4

Derivative of:

Answer 4

Question 5

Derivative of:

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

Exponential Growth and Decay

Answer 12

Question 13

Compound Interest

Answer 13

Question 14

Continously compounded interest

Answer 14

Question 15

Critical numbers

Answer 15

a number c in the domain of f, such that either f’(c)=0 or f’(c)= DNE

Question 16

Closed interval method (finding abs max/min)

Answer 16

1. Find the values of f at the critical numbers of f in interval
2. find the values of f at the endpoints of the interval
3. largest value= abs max, lowest value= abs min

Question 17

Mean Value Theorem

Answer 17

Question 18

First Derivative Test (for finding local max/mins)

Answer 18

1. if f’(c) goes from (+) to (-) at c = local max
2. if f’(c) goes from (-) to (+) at c = local min
3. if no change= no local min/max

Question 19

Concavity Test

Answer 19

• if f ¨(x)>0 in I, then = CU on I
• if f ¨(x)<0 in I, then = CD on I

Question 20

Inflection points

Answer 20

• if concavity changes at point P, then = POI

Question 21

Second Derivative Test

Answer 21

• if f’(x)=0, and f ¨(x)>0, then f has a local min at c
• if f’(x)=0, and f ¨(x)<0, then f has a local max at c