Show that has a maximum and minimum, but the maximum value is less than the minimum value.

F(x)=x+


Taking first derivative and equating it to zero to find extreme points.


F(x)=1-


X2=1


x=1,x=-1


now to determine which of these is min. And max. We use second derivative.


f||(x)=


f||(1)=2 and f||(-1)=-2


since f||(1) is +ve it is minimum point while f||(-1) is –ve it is maximum point


max value-> f(-1)=-1+=-2


min vaue-> f(1)=1+=2


hence maximum value is less than minimum value


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