Unit 3 Quiz

Question 1

The slope of one function is what(of the derivative of that function)

Answer 1

The y value of the derivative of that function

Question 2

If you identify the horizontal tangent lines of f you can find what for f’

Answer 2

You can find the zeroes of f’

Question 3

to don’t relative min value(aka why value) what do u do with the x value your already found

Answer 3

plug back into the OG equation

Question 4

2nd derivative test mathematically

Answer 4

first use 1st derivative to find critico al numbers
then find second derivative
plug in those critical numbers into second derivative
if you get a positive number that means it is concave up
if you get a negative number that means it is concave down

Question 5

if f is constant what is the first derivative of f

Answer 5

0(slope of f)

Question 6

if f is concave up what is f’

Answer 6

increasing

Question 7

if f is concave down what is f”

Answer 7

negative

Question 8

When is f” 0on a behavior table

(The options are pos, neg, 0)

Think of f graph in relation to

Answer 8

It is 0 when f is linear

Question 9

There is no value of X in the open interval -1 to 3 at which a person of X is equal to blank explain why this does not violate the mean value theorem

Consider cusps in holes in the graph

Answer 9

If it’s not differentiable X equals 02 to a sharp corner does the mean value theorem cannot be applied on the interval -1 to 3

Question 10

When asked if the graph of f is decreasing and concave down do what

Answer 10

Make BOTH sign charts then align the numbers!

Question 11

When using calculator to graph both h’ and h’’ do what

Answer 11

Draw your own graph and overlap the two so you can see the visuals at the same time, make sure to identify critical points too

Question 12

How to find POI on f(for f)

Answer 12

In the middle of the change fo slopes - that point where there is a vertical tan line

Question 13

How to find the POI of f (using f’)

Answer 13

Min and max on f’ graph

Question 14

How to find POI for f (using f’’)

Answer 14

Points on the x-axis, the zeroes

Question 15

How to find relative extrema-min/ max for f (using f’)

Answer 15

It is the critical points

Question 16

Extreme value theorem

Extreme aka absolute

Answer 16

A f(x) THAT is continuous on closed interval must have an absolute max or min

Question 17

How to write extreme value theorem FRQ

Answer 17

If f is continuous on [-1,3] then there exists a number c such that f(c)greate than or equal to( for an absolute max) or less than or equal to (for an absolute min) for all #’s x in [a,b]

Question 18

MVT

Answer 18

If f is continuous on [a,b] and differentiable on (a,b) than there exists at least 1 #c such that f’c = f(b)-f(a)/b-a

Question 19

Idea of MVT

Answer 19

The instantaneous rate of change at one point should be equal to the average rate of change

Question 20

1st derivative test

Answer 20

A critical point of f(x) is a relative min if f’(x) changes from negative to positive and for relative max vice versa

Question 21

Where are the values for absolute maximum and min

Answer 21

Endpoints or critical interior points

Question 22

What is first derivative test used for

Answer 22

Relative min and max

Question 23

What test do you sue for relative mina and max

Answer 23

First derivative

Question 24

What test do you use for extrema, absolute max/min?

Answer 24

Candidates test

Question 25

Candidates test

Answer 25

Still use f’ for candidates test

Identify critical points on the graph as endpoints or relative min and max aka f’ zeroes

Question 26

What si the order of the derivative

Increasing pos

Answer 26

Increasing/ deceasing - positive/negative - Ccu/ccd

Question 27

The graph of f is concave up when it’s derivative

Answer 27

Is increasing

Question 28

Points of inflection are

Answer 28

Extreme rates of change, max/ min value of a derivative

Question 29

2nd derivative test rules criteria(can on,y be used when …)

Answer 29

The 2nd D can only be used when

F has a critical point at x=a and f’(a)=0

Question 30

The 2nd D test does NOT work When (think ab graph of f)

Answer 30

f”(a)>0 or vice versa

Or if the slope(f’) is undefined

Question 31

When do we use 2nd D test most often amd why

Answer 31

On problems with tables because we can’t compare values of f’ to the left and right of the critical point

Question 32

following functions of x is guaranteed by extreme value thrm to have an absolute max on the interval consider

Answer 32

consider if those functions can be undefined in denominator, if so they do not work

Question 33

fewest possible number of values of c in the MVT such that f’c = 6

Answer 33

try every average rate of change for all values since instantaneous rate(f’c) of change equals average rate of change such that you get 6

Question 34

when dealing with mean value theorem MCQ answer must have

Answer 34

instantaneous rate of change and average rate of chabge

Question 35

derivative of e^x

Answer 35

e^x

Question 36

if f(x) is 1/x^2 and you are asked to find the min/max valued for f on [0,3] what do you do
FRQ

Answer 36

realize that f has a hole at 0 which is between 0 and 3 therefore the EVT can’t be applied you’d say:
since f(x) is rational func and continuous everywhere except x=0 the EVT cant be applied

Question 37

where f’(x)=0 and f’(x)= DNE

what are these points called

Answer 37

critical numvers

Question 38

for candidates test what do you do in your chart

Answer 38

put in values of critical and endpoints then plug those into the ig function and the highest y value is the absolute max and the lowest is the absolute min

Question 39

derivative of lnx

Answer 39

1/x

Question 40

what is the domain for ln x

Answer 40

x must be greater than 0

Question 41

tangent line is what rate of change

Answer 41

instantaneous

Question 42

secant lien is what rate of change

Answer 42

average

Question 43

how do you prove f(x) is differentiable in MVT

Answer 43

find f’(x) see if it’s differentiable(aka polynomial not rational)

Question 44

To find all values of c in MVT

do what

Answer 44

1) write f(x) is continuous on closed interval
2) find f’(x) and if so write that it’s differentiable on open interval
3) do f(b)-f(a)/b-a and set it equal to f’(x)
4) solve for x
5) x is the same thing as c as long as it fits in the interval

Question 45

cos x = 0

what is x

Answer 45

x is radians

pi/2, 3pi/2

Question 46

cosx-sinx cna be simplified to

Answer 46

cos x = sin x -> cosx/cosx = sinx/cosx -> 1=tan x