unit 3

Question 1

quotient rule

Answer 1

f’(x) = [h’(x)g(x) - h(x)g’(x)] / [g(x)]^2
- h(x) is top
- g(x) is bottom

Question 2

chain rule

Answer 2

(n)(orig eqn)^n-1 (derivative of orig eqn)

Question 3

absolute maximum/minimum

Answer 3

highest/lowest point reached by graph

Question 4

local maximum/minimum

Answer 4

highest/lowest point reached by graph within a domain

Question 5

extreme value theorem

Answer 5

if we limit the domain, there will be an absolute max/min in hat domain

Question 6

fermat’s theorem

Answer 6

there is a local max/min whenever m=0

Question 7

critical points + how to find them

Answer 7

• where m=0
• maxes/mins
• first derivative, then factor, then set to 0 and solve for x, then plug in x to orig eqn to find y

Question 8

how to find absolute max/min on equation WITH interval

Answer 8

• first derivative, solve for x, find y
• plug in interval values to find y
• roughly sketch coordinates and label abs. max/min and local max/min

Question 9

relatationship btwn function nd first derivative

Answer 9

critical pts on orig is x-ints on first derivative graph

Question 10

how to find interval of increase? (i.e. when is temp increasing)

Answer 10

1. first derivation
2. solve for variable
3. make table and do first derivation test

Question 11

horizontal asymptote

Answer 11

• if denom degree is greater, then y=0
• if same, divide leading coefficients

Question 12

vertical asymptote

Answer 12

zero of the denominator

Question 13

curve sketching

Answer 13

1. asymptotes
2. x and y intercepts + domain
3. first derivative (critical pts) + find y-val
4. second derivative (inflection pts) + find y-val
5. number line + table (x-ints and vertical asymptotes get crossed out)
6. graph (label + rmbr horizontal asymptote y=0)

Question 14

quadratic formula

Answer 14

-b+-sqrt(b^2-4ac over 2a