strictly concave up function

Jul 2009
127
0
suppose that f : R-->R is strictly concave up, strictly increasing function with a zero t satisfying a<t< b
Which of the following are true
1.f(b)<0
2.f(b)=0
3.f(b)>0
4.f(a)<0
5.f(a)=0
6.f(a)>0
7.impossible to determine

can someone help me with this
 
Last edited:

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
I would feel better about answering if you had shown some attempt yourself!

Consider the function \(\displaystyle f(x)= x^2- 1\) with
i) a= 0, b= 2
ii) a= -2, b= 0
 
Jul 2009
127
0
i don't understand what i'm supposed to do
 

Plato

MHF Helper
Aug 2006
22,507
8,664
suppose that f : R-->R is strictly concave up, strictly increasing function with a zero t satisfying a<t< b
Which of the following are true
1.f(b)<0
2.f(b)=0
3.f(b)>0
4.f(a)<0
5.f(a)=0
6.f(a)>0
7.impossible to determine
Do you know what a strictly increasing function means?
 
Jul 2009
127
0
upward sloping i think not sure what zero t means
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
upward sloping i think not sure what zero t means
f(x) is a strictly increasing function. that tells you that if a < t < b , then f(a) < f(t) < f(b)

"zero t" means f(t) = 0
 
Jul 2009
127
0
ok so...
1.f(b)<0 false
2.f(b)=0 false
3.f(b)>0 true
4.f(a)<0 true
5.f(a)=0 false
6.f(a)>0 false