Question

i need to find the interval of concavity of f(x)=(-2x^2+5x-1)/(2x-1)
for my f''(x) I got 8/(2x-1)^3
my concave down interval answer is
(-Infintiy,1/2)u(1/2,Infinity) but it says im missing the concave up i believe it does not exist?

Answer 1

my f'(x)=(-4x^2+4x-3)/(2x-1)^2

Answer 2

and f''(x)=8/(2x-1)^3

Answer 3

yup, you are correct, so, unless x = 1/2 which lead to f'' undefined, we have a table like that