Question

Sketch the graph of a function f(x) for which f(x) > 0, f’(x) > 0, and f’’(x) > 0 on the entire domain of f ?

Answer 1

@SolomonZelman

Answer 2

Hello!

Answer 3

Heya! :D

Answer 4

I check polynomial wouldn't work.
It would have t be even to make f(x)>0,
but f'(x) would be >0 at least for some x.

Answer 5

it is probably a square root

Answer 6

a very famous function works

Answer 7

famous function?

Answer 8

I get something like
\(\color{#0000ff }{ \displaystyle f(x)=\sqrt{x^3+3} }\)

Answer 9

a function all should know

Answer 10

yes pliz

Answer 11

\[\Large f(x)=e^x\]

Answer 12

Oh...

Answer 13

yes of course :))

Answer 14

I thought maybe
\(\color{#0000ff }{ \displaystyle f(x)=\sqrt{x+3}+3 }\)
fits

Answer 15

assuming that f'(x) doesn't have to be defined everywhere where f(x) is defined

Answer 16

the second derivative of that function is not positive

Answer 17

yes, the power....

Answer 18

we can make it positive... if we make a power bigger but of same nature, perhaps

Answer 19

with the cubed...then yes

Answer 20

\(\color{#0000ff }{ \displaystyle f(x)=\sqrt{(x+3)^5} +4 }\)

Answer 21

yes or cubed... i did 5th power just to secure myself

Answer 22

:| A lot is happening xD

Answer 23

do you have any questions about anthing in (or outside) the thread?

Answer 24

Not anything in this thread, anymore, but I have a few questions about other things in calc entirely xD

Answer 25

ok:)

Answer 26

I hope I am denoting things correctly.

Answer 27

I think I have extracted the general solution for this...

\(\color{#0000ff }{ \displaystyle y=a^{\Large x} ;\quad a>1}\)

\(\color{#0000ff }{ \displaystyle y=\sqrt[\Large 2b]{(x+5)^{\Large 3b+2m}};\quad b,m\in\mathbb{N} }\)

Answer 28

don't want to get to complicated tho... you might as well take e^x ...

Answer 29

good luck

Answer 30

Ok xD thanks guys

Answer 31

yw