I get the concavity backwards....I get cu (- infinity,1) cd (1, infinity)
but the answer says cd (-infinity, 1) cu (1, infinity)...I might just be getting the derivitives wrong
The problem is t2/t-1
For f'(x) I get -t^2+2t/(t-1)^2 or -t(t-2)/(t-1)^2
For f''(x) I get -2(2t+1)/(t-1)^3
I set f''(x) equal to zero...i use the denominator right? (t-1)= 0...t=1
For the critical number i get 1...plug in my test points and i get it wrong..so i figure it has to be my derivatives...Can someone work out the whole problem so i can see where i'm messing up..thanks
To determine the concavity of a function you normally calculate f''(x) = 0 to get the point where the concavity changes (point of inflection).
In your case this method isn't possible because the function has no point of inflection. Therefore you have to use the definition of concavity as I have shown in my previous post.
In general: A quotient is zero if the numerator is zero and the denominator is unequal to zero. The second derivation of your function is a constant (2) which can't be zero.