Semester 1 Vocab

Question 1

dsin(x) =

Answer 1

cos(x)

Question 2

dcos(x) =

Answer 2

-sin(x)

Question 3

dtan(x) =

Answer 3

sec^2(x)

Question 4

dcsc(x) =

Answer 4

-csc(x)cot(x)

Question 5

dsec(x) =

Answer 5

sec(x)tan(x)

Question 6

dcot(x) =

Answer 6

-csc(x)

Question 7

dsin^-1(x) =

Answer 7

1/(1-x^2)^1/2

Question 8

dcos^-1(x) =

Answer 8

-1/(1-x^2)^1/2

Question 9

dtan^-1(x) =

Answer 9

1/(1+x^2)

Question 10

if f is continuous on a closed interval [a, b], the f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in [a, b].

Answer 10

Extreme Value Theorem

Question 11

to find the absolute maximum and minimum values of a continuous function f on a closed interval [a, b]:
1. find the values of f at the critical numbers of f in [a, b]
2. find the values of f at the endpoints of the interval
3. the largest of the values from steps 1 & 2 is the absolute maximum

Answer 11

Closed Interval Method

Question 12

if f is differentiable on the interval [a, b], then there exist a number c between a and b such that:
f’(c) = (f(b) - f(a))/ (b - a)

Answer 12

Mean Value Theorem

Question 13

suppose c is a critical number of a continuous function f.
a) if f changes from + to - at c, then c is a local maximum
b) if f changes from - to + at c, then c is a local minimum
c) if f does not have a sign change at c, then there is not a local max or min at c

Answer 13

1st Derivative Test

Question 14

suppose c is continuous near c.
a) if f’(c) = 0 and f’‘(c) > 0, f has a local min at c
b) if f’(c) = 0 and f’‘(c) < 0, f has a local max at c

Answer 14

2nd Derivative Test

Question 15

suppose function f and function b are differentiable and g’(x) can’t equal 0 near a (except possibly at a)

Answer 15

L Hop

Question 16

a function F is called the antiderivative of f on an interval I if F’(x) = f(x) for all x in the interval I

Answer 16

Antiderivative

Question 17

if f is a polynomial or rational function (and a is in the domain of f), then you can take the limit using direct sub

Answer 17

Direct Sub Property

Question 18

suppose f is continuous on the closed interval from [a, b] and let N be any number between f(a) and f(b), where f(a) can’t equal f(b), then there consists a number c in [a, b] such that f(c) = n

Answer 18

Intermediate Value Theorem

Question 19

a number c in the domain of f such that either f’(c) = 0 or f’(c) doesn’t exist

Answer 19

Critical Number