What is the extreme h(x,t)=1.5+log_{3}(x)(t+1) ?

The extreme h(x,t)=1.5+log_{3}(x)(t+1) is Saddle(1,-1)

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extreme h(x,t)=1.5+log_{3}(x)(t+1)

extreme points

h (x, t) = 1.5 + lo g_{3} (x) (t + 1)

Saddle (1, - 1)

Solution steps

Find the critical points:

(1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, t) = - \frac{1}{ln ^{2} ( 3 ) x ^{2}}

Check the sign of at each critical point

Check critical point

(1, - 1) :

Saddle

Saddle (1, - 1)

\frac{3200}{x} + 200 + 50 x

f (x y) = x^{2} + 4 y^{2}

f (x, y) = - 2 x^{2} + 16 x - y^{2} + 6 y - 30

f (x) = 2 x - \frac{1}{2} (\frac{x}{50})^{2} - 1000

f (x, y) = - 6 x^{2} - 3 x y - 7 y^{2} - 90 x + 4 y + 8

What is the extreme h(x,t)=1.5+log_{3}(x)(t+1) ?
The extreme h(x,t)=1.5+log_{3}(x)(t+1) is Saddle(1,-1)