Question

Examine the graphs below and determine which is the graph of f(x), f ′(x), f ′′(x):
a. A is f ′′(x), B is f (x), C is f ′(x)
b. A is f ′(x), B is f(x), C is f ′′(x)
c. A is f(x), B is f ′′(x), C is f ′(x)
d. f(x) is not differentiable so the graphs of f′(x) and f′′(x) cannot be displayed

Answer 1

Your idea?

Answer 2

Hint: check one by one, if f"(x) >0, f(x) has concave up,
if f"(x) <0, f(x) has concave down.

Answer 3

Reading the graph is not hard, just practice, show your work, please. It is YOUR problem.

Answer 4

what about ones that have multiple maxima and minima

Answer 5

since a has concave down it could be second derivative?

Answer 6

Actually, if you work on f(x) and f"(x) and figure out they are matching, 90% that is the right one. f'(x) just make sure that is 100% correct.

Answer 7

I dont understand how to figure this out

Answer 8

Suppose a is the right answer, that is B is f(x) A is f"(x) , let check:
from - infinitive to -0.5, f(x) has concave up, right? and f"(x) is >0, Bingo

Answer 9

I am not trying to fish for an answer I just want to know how to do this problem

Answer 10

next is from -0.5 to 0
f"(x) <0, and f(x) has concave down, oh yea!!! right again.

Answer 11

then from 0 to 0.75 f"(x) <0 still, and f(x) has concave down. so far so good, right?

Answer 12

and the leftover works well also. I mean from 0.75 to infinitive, f"(x) >0 and f(x) has concave up again.

Answer 13

Potential candidate is A)
Now check f'(x)

Answer 14

how to check?? Hint : minimum, maximum points. YOu work, please

Answer 15

If you don't know how to check, fell free to ask.

Answer 16

I don't understand how one can tell

Answer 17

Do you understand what I did for f"(x) and f(x)?

Answer 18

I have no idea

Answer 19

ooooooooooooops!!!

Answer 20

do you know what is concave up/ down?

Answer 21

no and i want to know how this helps you figure it out what math is behind it

Answer 22

ok, I guide you how :)
I check option A) it says B is f(x) A is f"(x)