Question

to determine the intervals where a function is concave up and concave down, the first step is to find all the x values where (select all that are needed):
○f(x)=0
○f(x) is undefined
○f(x)=0
○f(x) is undefined
○f(x)=0
○f(x) is undefined

Explanation:

To find intervals of concavity (concave - up and concave - down) of a function, we first find the inflection points. Inflection points occur where the second - derivative \(f''(x)=0\) or where \(f''(x)\) is undefined. So, we need to find the \(x\) - values where \(f''(x) = 0\) and where \(f''(x)\) is undefined.

Answer:

\(f''(x)\) is undefined, \(f''(x)=0\)