Concavity-TheoremO If f"(x)>0 for all value of x in I, then fisconcave up on IO If f"(x)<0 for all value of x in I, then fisconcave down on I
Concavity - ⚫Theorem If f ’’(x)>0 for all value of x in I, then f is concave up on I If f ’’(x)<0 for all value of x in I, then f is concave down on I
InflectionPointsDefinitionIf fis continuous on an open intervalcontaining a value xo and if f change thedirection of concavity at the point (xo, f (xo) )then we say that f has an inflection point atXo and we call the point (xo, f(xo) ) on thegraph of f an inflection point of f
Inflection Points ⚫Definition If f is continuous on an open interval containing a value x0 and if f change the direction of concavity at the point (x0 , f (x0 ) ), then we say that f has an inflection point at x0 and we call the point (x0 , f (x0 ) ) on the graph of f an inflection point of f