What is the extreme V(A,t)=A^t ?

The extreme V(A,t)=A^t is Saddle(1,0)

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extreme V(A,t)=A^t

extreme points

V (A, t) = A^{t}

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial A ^{2}} = A^{t} ln^{2} (A)

D (A, t) = t^{2} A^{2 t - 2} ln^{2} (A) - t A^{2 t - 2} ln^{2} (A) - A^{2 (t - 1)} - 2 t A^{2 t - 2} ln (A) - t^{2} A^{2 (t - 1)} ln^{2} (A)

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

f (x) = x^{3} + 32 x^{2} - 6 x + 8, - 4 \leq x \leq 2

f (x) = x + \frac{x}{9}

280

x^{4} + 3 x^{3} - 5 x^{2} - 6 x + 6

f (x) = 3 x^{3} - 36 x^{2} + 108 x + 4, 0 \leq x \leq 9