Question

how to find points of inflection... help?

Answer 1

the figure below shows the graph of f', the derivative of the function f, on the closed interval from x=-2 to x=6. the graph of the derivative has horizontal tangent lines at x=2 and x=4. find the x-coordinate of each of the points of inflection of the graph of f. justify your answer.

Answer 2

@MrNood

Answer 3

i know that points of inflection are when the function is continuous and the concavity changes

Answer 4

i'm just unsure how to find inflection points from a graph

Answer 5

I am a bit rusty on this but:

I think that f''(x) =0 for minima,maxima AND POI

So the points where the slope of the graph of f'(x) = 0 are 1 of those thre types of point.

There is only one point on the graph where the slope =0

if the sign is the sign of f'(x) is the SAME on either side of that point then it is a POI

Answer 6

OOPS correction

there are TWO points where slope is 0

Answer 7

x=2 and x=4 have slope of 0

Answer 8

what do you mean by the signs?

Answer 9

look at the value of f'(x) either side of the points x=2 and x=4

if the value is negative on both sides OR positive on both sides then it is POI

(I suggest you check this -as it is a while since I learnt this)

Answer 10

so both x=2 and x=4 are poi because the values on both sides are negative

Answer 11

or is it just x=2 is a poi since x=4, the value becomes positive after (5,0)

Answer 12

I think it is both, because just each side of the point the sign is negative in both cases

Answer 13

BUT please check and be sure YOU understand

Answer 14

of course thank you for attempting to help me

Answer 15

look for an example that relate to this qustion it should help you

Answer 16

i'm looking for one (:

Answer 17

what grade level is this?

Answer 18

it's ap calc ab. im in 12th grade

Answer 19

@foreverjb
I have mislead you above

my answer is not correct

see here:
http://www.statistica.com.au/differentiation_max_and_min.html

Answer 20

oh

Answer 21

oh no wonder i did not understand this i'm in 8'th

Answer 22

haha you have a few years to go (:

Answer 23

it is f'(x)=0 for maxima minima and POI

so all the points where your graph touches or crosses the x axis are those points.

Answer 24

ohhhh okay so x=2 and x=5

Answer 25

but you then have to decide whether they are POI or max/min

f''(x) = 0 for POI

Answer 26

how do i find f"(x)?

Answer 27

f"(x) = 0 is where your graph has slope =0

Answer 28

my graph has f' not f" tho

Answer 29

yes - but you can see where f"(x) = 0 is where your graph has slope =0

i.e. the max or min points of f'(x)

Answer 30

max is (6,4) and min is (-2,-3)

Answer 31

for a POI
f'(x)=0
f''(x)=0

Answer 32

okay, i got that part

Answer 33

so there is only one point where that is true...

Answer 34

x=2

Answer 35

correct

It's coming back to me now! :-)

Answer 36

thank you for all your help omg