unit 1

Question 1

rules of infinite limits of trig functions

Answer 1

lim sin(x) x-0= DNE

Question 2

derivatives of trig functions

Answer 2

sin=cos(x)
cos= -sin(x)
tan= sec^2(x)
cot= -csc^2(x)
sec= sec(x)tan(x)
csc= -csc(x)cot(x)

Question 3

what is a critical number

Answer 3

derivative of a function equals zero or does not exist

Question 4

what is the extreme value theorem

Answer 4

for any function that is continuous on a closed interval, there will be an absolute max/min

Question 5

to find absolute max/mins:

Answer 5

1. find all critical numbers
2. plug in critical numbers and endpoints into the function
   - largest results is the absolute max, smallest is mins

Question 6

what is the mean value theorem?

Answer 6

for a function that is continuous on [a,b] and differentiable on (a,b) there will be at least one point,c, on [a,b] where the average slope equals the instantaneous slope

Question 7

MVT formula

Answer 7

f(b)-f(a)/b-a = f’(c)

Question 8

what is rolle’s theorem

Answer 8

if f(x) is differentiable on (a,b) and f(b)=f(a), f’(c)=0 for some c on (a,b)

Question 9

what is the first derivative test

Answer 9

if f(x) is differentiable on an open and continuous interval, except possibly at c, then f(c) can have a relative max, min, or none at c=x.

Question 10

steps of the first derivative test

Answer 10

1. find all critical numbers
2. create an f’(x) chart/line
3. classify your critical numbers in context of the problem (sentence)

Question 11

the points where concavity changes are always found when the second derivative is ____

Answer 11

0 or DNE

Question 12

for points of inflection the _____

Answer 12

SECOND derivative is equal to zero