Inflection Points o Definition If fis continuous on an open interval containing a value xo and if fchange the direction of concavity at the point (xo f(x)), then we say that fhas an inflection point at xo and we call the point (xo,f())on the graph of fan 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
Relative Extrema Definition OA function fis said to have a relative maximum at xo if there is an open interval containing xo on which fo)is the largest value,i.e.fxo)x)for all x in the interval OA function f is said to have a relative minimum at xo if there is an open interval containing xo on which f(xo)is the smallest value,i.e.fxo)x)for all x in the interval
Relative Extrema ⚫Definition A function f is said to have a relative maximum at x0 if there is an open interval containing x0 on which f(x0 ) is the largest value, i.e. f(x0 )≥f(x) for all x in the interval A function f is said to have a relative minimum at x0 if there is an open interval containing x0 on which f(x0 ) is the smallest value, i.e. f(x0 )≤f(x) for all x in the interval