Derivative Constant: No Intervals of Concavity

[orangesang]

ok. So if the second derivative of a function is equal to a constant and i want to find any intervals of concavity there is none right? therefore no infelction points nor relative and/or absolute extrma

f(second derivative)(x)=2

 

[CompuChip]

A function is called concave if the second derivative is negative. So if f'' is constant, then it is everywhere either concave, or convex (or f'' = 0). Inflection points are those where the derivative changes sign, so indeed there are none. The extrema have to do with the first derivatives of the function. For example, I can make up a function f(x) such that f''(x) = 2 but which has a global minimum... can you?

 

[HallsofIvy]

For example, f(x)= x² has second derivative 2 and is convex for all x and has 0 as an absolute minimum.

f(x)= -x² has second derivative -2 and is concave for all x and has 0 as an absolute maximum.

Of course, neither of those has any inflection points.