What is the extreme z(b,v)=b^{2v} ?

The extreme z(b,v)=b^{2v} is Saddle(1,0)

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extreme z(b,v)=b^{2v}

extreme points

z (b, v) = b^{2 v}

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial b ^{2}} = 4 b^{2 v} ln^{2} (b)

D (b, v) = 8 v b^{4 v - 2} ln^{2} (b) (2 v - 1) - 4 (b^{2 v - 1} + 2 v b^{2 v - 1} ln (b))^{2}

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)