ap test ntk

Question 1

horizontal asymptote rules

Answer 1

f(x) = (ax^n)/(bx^m)
n<m HA @ y=0
n=m HA @ a/b
n>m NO HA

Question 2

definition of a derivative

Answer 2

f’(x) = lim(h=>0)

f(x+h) - f(x) / h

Question 3

alternate form of definition of a derivative

Answer 3

f’(x) = lim(x=>h)
f(x) - f(h) / x-h

Question 4

definition of continuity

Answer 4

• f(c) is defined
• lim (x=>c) f(x) exists
• lim (x=>c) f(x)=f(c)

Question 5

mean value theorem

Answer 5

if f is CONTINUOUS on [a,b] and DIFFERENTIABLE on (a,b), then there is a slope of a tan line of point c that equals the slope of the line from a to b

Question 6

intermediate value theorem

Answer 6

if f is CONTINUOUS on [a,b] and k is any number between f(a) and f(b), then there is at least one value c between a and b where f(c)=k

Question 7

definition of a critical number

Answer 7

if f’(c)=0 or if f’ is UND at c

Question 8

first derivative test

Answer 8

• find f’(x)
• uses ranges
• determines local max/min

Question 9

second derivative test

Answer 9

• find f”(x)
• uses ranges
• determines concavity

Question 10

definition of concavity

Answer 10

• f(x) is concave upward is f’(x) is increasing
• f(x) is concave downward if f’(x) is decreasing

Question 11

definition of an inflection point

Answer 11

• if f”(x)=0 or f”(x)=DNE
• if f”(c) changes signs from pos to neg / neg to pos
• if f’(x) changes from inc to dec / dec to inc

Question 12

first fundamental theorem of calc

Answer 12

integral of a to b of f’(x)dx = f(b) - f(a)

Question 13

second fundamental theorem of calc

Answer 13

the derivative of an integral with x and of f(t)
plug the x in for t and TAKE THE DERIV OF X

Question 14

average rate of change formula

Answer 14

f(b) - f(a) / (b-a)

Question 15

average value formula of f(x) on [a,b]

Answer 15

1/b-a ∫ f(x)dx

Question 16

displacement

Answer 16

∫ v(t) dt

Question 17

distance

Answer 17

∫ |v(t)| dt

Question 18

the graph of f is cont but NOT diff at x=c when

Answer 18

• sharp point / cusp
• vertical tangent line
• endpoint

Question 19

extreme value theorem

Answer 19

if f(x) is CONT on [a,b] the there is at least one max/min (horizontal lines are ALL max/mins)

Question 20

derivative of an inverse

Answer 20

1/f’(g(x))

Question 21

general solution for exponential growth and decay

Answer 21

y=Ce^(kt)

Question 22

differentials equation (Δy and dy equations)

Answer 22

Δy = f(x2) - f(x1)
dy = f’(x)dx

Question 23

value estimates ( f(1.2) )

Answer 23

• find f’
• create equation (y=mx+b)
• plug in estimate value for x

Question 24

instantaneous velocity

Answer 24

f’(x)
- use when the roc isn’t constant

Question 25

average velocity

Answer 25

( f(b)-f(a) ) / (b-a)
- can only use when the roc is constant

Question 26

e⁰

Answer 26

1

Question 27

ln(1)

Answer 27

0

Question 28

f(x) of a graph gives

Answer 28

• abs. max/mins
• use endpoints and CN

Question 29

f’(x) of a graph gives

Answer 29

• rel. / local max/mins
• use CN only

Question 30

f”(x) of a graph gives

Answer 30

• concavity
• use endpoints and CN

Question 31

inflection points

Answer 31

• when f’(x) goes from inc/dec
• when f”(x) goes from concave up/down

Question 32

when evaluating abs max/mins

Answer 32

use CN and endpoints

Question 33

distance

Answer 33

absolute value

Question 34

displacement

Answer 34

regular integral