# strictly concave up function

• Aug 8th 2010, 08:25 AM
dat1611
strictly concave up function
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
• Aug 8th 2010, 08:52 AM
HallsofIvy

Consider the function $f(x)= x^2- 1$ with
i) a= 0, b= 2
ii) a= -2, b= 0
• Aug 8th 2010, 08:59 AM
dat1611
i don't understand what i'm supposed to do
• Aug 9th 2010, 03:32 PM
Plato
Quote:

Originally Posted by dat1611
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?
• Aug 9th 2010, 03:52 PM
dat1611
upward sloping i think not sure what zero t means
• Aug 9th 2010, 03:58 PM
skeeter
Quote:

Originally Posted by dat1611
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
• Aug 9th 2010, 04:04 PM
dat1611
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