A function ƒ satisfies the following conditions: ƒ(7)=20, ƒ'(7)=2, and ƒ''(x)

Question

A function ƒ satisfies the following conditions: ƒ(7)=20, ƒ'(7)=2, and ƒ''(x)<o for x≥7. Which of the following are possible values for ƒ(8) and which are impossible? Explain
a) 20 b) 21 c) 22 d) 23 e) 24

anonymous · Answer

how come f`(x)<0  for x>=7 and f`(7)=2   !!

anonymous · Answer

this is Question from old exam?

anonymous · Answer

are u sure that x>AND=7

anonymous · Answer

let me double check

anonymous · Answer

yea it's same Question

anonymous · Answer

is it f` or f`` in the condition

anonymous · Answer

ƒ''

anonymous · Answer

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anonymous · Answer

the question ask about ƒ(8)??

anonymous · Answer

i know, but look at this drawing, what do you think now about f(8) ?

anonymous · Answer

ok, u got the key but I'm working on it.

anonymous · Answer

how do u know its opining down(bending down)??

anonymous · Answer

well i dont know what happens for x<7 (i just decided to draw it like this) 
but for x>7 we know that it goes down since f'' < 0 (the derivative is always getting lower)

anonymous · Answer

I'll show u how to use 7 in the graph

anonymous · Answer

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