Question

Assume the function f is such that f'' (x) > 0 for all values of x. Which one of following statement is true about f?

Answer 1

see picture

Answer 2

A can't be right think of \(e^x\)

Answer 3

I know it's not A or B

Answer 4

i guess it can't be C either,again think of \(e^x\) , no zeros, no critical point

Answer 5

and similarly D can''t be right, for the same reason
that leave E

Answer 6

of course if the critical number exists, and if \(f''>0\) this means it must be a local min
i guess it is also true that there can be at most one, since if \(f''>0\) that means \(f'\) is always increasing, so it cannot be zero more then once

Answer 7

how do u know that f behaves like e^x ?

Answer 8

the only info u have is f is concave up.. but it still can mean it crosses the xintercept right @satellite73

Answer 9

E is the correct ans..see,, it is given that rate of change of slope is always positive..
which means slope must be negative somewhere and is increasing as x increasing, hence it'll go from -ve to 0 to +ve,,which means minima..

Answer 10

I do understand there is a minima, and slope is always increasing
oh wait, i get it
since there is a minima, that means f'(x) = 0 , which means 1 critical point , is that right?

Answer 11

no one says it crosses the \(x\) axis

Answer 12

E says it has AT MOST one critical point, and IF it has one, it is a min

Answer 13

yea, i'm keep mixing up root and ciritical pt :/

Answer 14

again \(e^x\) is a good example
it has not critical point, and never crosses the \(x\) axis
it was an "if" statement

Answer 15

btw the critical point if it exists must be root of the derivative, it cannot be where the derivative is undefined
writing \(f''<0\) assumes that \(f''\) exists for all \(x\) and therefore \(f'\) exists for all \(x\) as well

Answer 16

@satellite73 hey, just a quck quesion. If f'' exist, f' cant be undefined rght

Answer 17

yes that is right
if \(f''\) exists then \(f'\) must not only be defined, it must be continuous as well

Answer 18

ok thanks!

Answer 19

now i have a question

Answer 20

what drink are you making?