Question

Given the graph of f'(x), the derivative of f(x), which of the following statements would be true about the graph of f(x)?
I. The graph of f does not have a point of inflection.
II. The graph of f has a point of inflection at x = 2.
III. The graph of f has a critical point at x = 2.

Answer 1

a. I only
b. II only
c. III only
d. I and III only

Answer 2

Please help, I really do need it.

Answer 3

please can you show us the graph of f'(x)?

Answer 4

@ganeshie8 @Hero @AravindG @nincompoop @iGreen @agent0smith @johnweldon1993 @sammixboo @Preetha @AnswerMyQuestions @YanaSidlinskiy @Conqueror @Michele_Laino @linn99123

Answer 5

I think that at x=2 there is an inflection point for f(x)

Answer 6

since for x<2 f'(x) is an increasing function, and for x> 2 f'(x) is a decreasing function. So at x=2 there is a descendant inflection for f(x)

Answer 7

Do you think any of the other answers are remotely correct?

Answer 8

I think the option b.

Answer 9

Okay...I am still a little sketchy because I'm on my second try and if I get it wrong than I can't make that problem up. Thanks.
Also, can you help me with this problem?

Answer 10

Use the graph of f(x) below to estimate the value of f '(3):

Answer 11

ok!

Answer 12

please is the graph of f(x) a parabola?

Answer 13

here's all the information i have regarding the problem

Answer 14

I understand that tha graph of f(x) is a parabola. Now from that graph I inferred the subsequent equation for f(x):
\[f(x)=-x ^{2}+9\]
so we have:
\[\frac{ d }{ dx }(-x ^{2}+9)=-2x\]
and at x=3, I get f'(3)=-6

Answer 15

thats not an answer tho

Answer 16

I think that your graph is not a parabola, so I think that:
since the slope of the tangent line has to be negative at x=3, my answer is -1.
the answer -5 can not be since the tangent line to your graph at x=3 is parallel to the bisector line of the II and IV quadrants

Answer 17

can i see if we can get other opinions to clarify?

Answer 18

@ganeshie8 @Hero @AravindG @nincompoop @iGreen @agent0smith @johnweldon1993 @sammixboo @Preetha @AnswerMyQuestions @YanaSidlinskiy @Conqueror @Michele_Laino @linn99123

Answer 19

ok!

Answer 20

@ganeshie8 @hartnn @Hero @cwrw238 @iGreen @uri @Preetha

Answer 21

Hey guys can you help I would really like a second opinion. Please?

Answer 22

@mathmate Can you give us your opinion, please?

Answer 23

It's the second problem

Answer 24

@familyguymath
Hey, I did some more checking.
I have erred in the definition of inflection point... Sorry.
An inflection point does not have to have f'(x)=0, even though it could be.
As long as f"(x)=0, it is an inflection point, which means that as long as concavity switched, it is an inflection point.
So you're right, (b) is the answer.
I apologize for having spent much of your efforts, but we both benefit from learning in detail.

Answer 25

Okay, thanks. But will you help us now on this new problem?

Answer 26

@mathmate

Answer 27

I'm sorry but I think that the slope of the tangent line at x=3, can be -5 @familyguymath

Answer 28

I agree with @Michele_Laino 's conclusions.
We are looking at an estimate, which could be \(f'(x)=f(x)-f(x-1)\) which equals (9-4)=5.
Michele has given a more exact answer by fitting the curve as a parabole over three points,
(0,9),(1,8),(2,5),(3,0) which gives f(x)=9-x^2, and f'(x)=-2x, => f'(3)=-6 (as before).

Answer 29

*parabola

Answer 30

So you both think its the -5 and the -1

Answer 31

because @Michele_Laino you put that a little while ago

Answer 32

I calculated the slope as well and got and -6 but that # wasnt there so the closest # was the -5

Answer 33

Estimates of slopes are better if it is symmetrical about the point inquestion, for example, f(3+0.5)-f(3-0.5)/(+0.5- -0.5).
In this case, the graph ends at x=3, so we can more or less approximate.

Answer 34

Hey guys but the regular slope is -5

Answer 35

I don't know where -1 comes from, but -5 \(could\) be an answer obtained by approximating
f'(3)=(f(3)-f(2))/1, graphically.

Answer 36

ohh wait yah thats right

Answer 37

@Michele_Laino :) I think you just confirmed graphically that the slope is -6. :)

Answer 38

wait, I'm sorry I have made an error in my drawing.

Answer 39

I think that -5 is it? You guys agree?

Answer 40

The question calls for an estimate, so anything from -5 to-7 \(should\) be acceptable.

Answer 41

Will you guys check other problem?

Answer 42

I agree that a good estimate is -6, but I can live with -5 because f(3)-f(2)=-5

Answer 43

here in my picture below, I have drawn the tangent line at graph at x=3, the bisector of the II and IV quadrants, and the line whose slope is -5

Answer 44

Can you remind me of the "other problem"?

Answer 45

For what values of x is the graph of y= (2)/5-x concave upward?

Answer 46

i just want to know if x<5 was correct or not

Answer 47

For all values of x where f"(x)>0.
Is it \(\dfrac{2}{5-x}\) ?

Answer 48

yes

Answer 49

Well,
f(x)=\(\dfrac{2}{5-x}\), f"(x)=\(\dfrac{4}{(5-x)^3}\)
so x<5 will be all values x s.t. f"(x)>0.
Yes, x<5 is correct.