The question is : Find an F(x) where fprime(-1) = 1/2 , fprime(0) = 0 and fdoubleprime>0 if it doesnt exist prove why. I cannnot explain it that well but here i go, i feel there is no equation that can be made for this. For an equation for be concave up on all intervals it must be in the form Ax^multipleof2 + B^multipleof2 + C^multipleof2 + etc etc etc..... + Dx + E, where A and B and C... are positive constants I say this because f double prime will onyl be positive for all x if the second dirivitive has only positive constants or terms of x^multipleof2. Then the first dirivitive will leave you with x^odd number + a constant, f(-1) must be equal to 1/2, so it must be positive since x^oddnumber will be negative. but then when it says fprime(0) = 0 this cannot be because you will have 0^oddnubmer + constant. blah thats as far as i could take it im not sure if it makes sense.. but can someone help me on the correct path.