Question

2. State what the following conditions tell about the graph of function f(x).
a. f'(-1)=f'(1)=0
b. lim f(x)= -2
c. lim f(x)= infinity
d. f'(x)<0 on (-infinity, 3)
e. f'(x)>0 on (3, infinity)
f. f"(x)>0 on (-infinity, -1)
g. f"(x)<0 on (-1, infinity)

Answer 1

what are you suppose to do here? draw f(x) with these conditions?

Answer 2

brb....

Answer 3

the only thing the problem says is to state what the following conditions tell about the graph of the function

Answer 4

ok

Answer 5

we don't need to draw it then? that's easy...

Answer 6

so for a)... what do you think that statement means?

Answer 7

f' is zero at x=-1 and x=1... we did this in the previous problem...

Answer 8

do you know what c is called when f'(c) = 0 ?

Answer 9

ok sorry my computer was being dumb!~

Answer 10

would the graph be a parabola?

Answer 11

why would u say that it's a parabola?

Answer 12

but no i cant think of what c would be

Answer 13

because it has to go through 1 and -1

Answer 14

that's what i thought at first but look closely... it's not f(-1)=f(1)=0, it's f'(-1)=f'(1)=0

Answer 15

what does that mean?

Answer 16

it means you have a local max/min at x=-1 and x=1... those are critical numbers....

Answer 17

oh

Answer 18

remember like how we did in the last problem?

Answer 19

but i though we plugged that into the equation, there is no equation

Answer 20

it's ok... that's just what that statement means... isn't that what the question asked?

Answer 21

i copied and pasted the problem in so if that what you get out of it then yes :)

Answer 22

so does that say that that graph makes a curve? sorry i am very confused on this problem

Answer 23

yes... at x=-1, x=1 the slope of the tangent line will be zero there...

Answer 24

uh huh

Answer 25

so it can look like this...