Question

The graph of f(x) is shown on the interval . [-6,6] pls see the attachment

List the points at which the derivative,f'(x), is equal to zero.

State the subintervals of (-6,6) on which the derivative, f(x) , is positive, using interval notation and ``U'' to denote union

State the subintervals on which the derivative,f(x) , is negative.

Answer 1

Do you understand when f'(x) = 0

Answer 2

This question is testing your understanding of first derivative purpose :)

Answer 3

no i don't understand

Answer 4

Can you take a look of your notes, textbook, study resource before response " no, ....." :0

Answer 5

i left my book back home, and im on a vacation, i've tried to find some examples for these on online but could not find any :(

Answer 6

trust me i have done everything but could not find any thing that explains how to find f'(x)=0

Answer 7

i know how to find f(x)

Answer 8

but not f'(x)=0

Answer 9

How about f'(x) >0 ==> f(x) ...?

Answer 10

infinity?

Answer 11

if it was just a equation i can find then like f'(x)=4x-5

Answer 12

but with graph and a picture no idea

Answer 13

No, the meaning of the first derivative test is to find out if the graph is DECREASING / INCREASING!
When f'(x) > 0 --> the graph f(x) is .... ( guess :) )

Answer 14

increasing

Answer 15

Yup, common sense :)
Now f'(x) < 0 ---> f(x) is .....?

Answer 16

that is simple, it is decreasing

Answer 17

100% agree, nothing as simple as first derivative test :D
Then f'(x) = 0 ---> f(x) is ....?

Answer 18

0

Answer 19

Knowing that f(x) is the SHAPE of the graph!

Answer 20

its like -5.7, -5.7 ish and 0

Answer 21

Do you know the relation between tangent line and first derivative test?

Answer 22

don't remember it yet :)

Answer 23

Now, another common sense hint!
f'(x) = 0 is between f'(x) < 0 and f'(x) > 0
-> f(x) is ....

Answer 24

nope don't get it. its still 0?

Answer 25

Does critical point max, min ring a bell?

Answer 26

f(x) is not 0?

Answer 27

If it's, I won't still give out the hints, reminder the basic concept :/

Answer 28

the x is not clear on the graph there is no way to find them out except 0

Answer 29

I guess I just hand you the solution for now, but you should be aware all the basis concept of first derivative test ( in/decreasing, max/min, tangent line)

Answer 30

On the interval [ -6,6] , f'(0) at ( -4, 2), (4,2)

Answer 31

yeah definitely, i spend all day at the tutor lab.

Answer 32

I don't know how you miss the short sweet concept of simple first derivative test::
f'(x) > 0 --> graph f(x) is INCREASING
f'(x) < 0 --> graph f(x) is DECREASING
-> f'(x) = 0 ---> CRITICAL Points!
very practically common sense :)

Answer 33

i see, now i know.

Answer 34

how about subintervals of (-6,6) on which the derivative f(x) is positive

Answer 35

Can you see where the graph increasing / decreasing :0

Answer 36

should be (-6,-4)U(0,4)

Answer 37

got it very easy

Answer 38

just never been taught

Answer 39

Why you have this homework when you just never been taught :0

Answer 40

yeah ha you are right, i guess i was not paying attention.

Answer 41

ok thank you again!!

Answer 42

I hope my brief summary helpful for you in someway!

Answer 43

oh sure yeah, it was very helpful, made me think

Answer 44

At least you attempt to memorize the colorful boxes from your textbook, then you'll be fine :)

Answer 45

find f'(x) if f(x)=1/x the answer is f'(x) is -1/x^2 can you briefly explain the steps?

Answer 46

Yeah, people know me for being rough, mean, ... as long as I reach my goal of forcing the asker to THINK!

Answer 47

i know the formula its f(x+h)-f(x)/h

Answer 48

It's straight forward power formula:
( x^n )' = n x^ ( n-1)

Answer 49

i see

Answer 50

f(x) =1/x = x ^ (-1)
-> f'(x) = - x^ (-2) = -1/ x²

Answer 51

I'll get off now! My suggestion is If you'd like to continue with your Math study, memorize the formulas and rules, PLUS PRACTICE on the key concepts is the MUST :)

Answer 52

good night! please help me later when you see me !! i will continue with my math!!