Write necessary condition for a point = c to be an extreme point of the function ().

Question

Write necessary condition for a point  = c to be an extreme point of the function ().

Philoid · Accepted Answer

Condition 1:- If f (x) is continuous and f’(x) and ’ exists then all points where (’(x)=0 and ”( x)>0) or (f’(x)=0 and f”( x)<0) are extreme points.

Condition 2:- If f(x) is continuous and defined in [a,b] and condition 1 is not satisfied, then points a and b are extreme points.