What is the extreme f(x,y)=(-2x)/(sqrt(y))+e^x-13 ?

The extreme f(x,y)=(-2x)/(sqrt(y))+e^x-13 is Saddle(0,4)

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extreme f(x,y)=(-2x)/(sqrt(y))+e^x-13

extreme points

f (x, y) = \frac{- 2 x}{y} + e^{x} - 13

Saddle (0, 4)

Solution steps

Find the critical points:

(0, 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{3 x}{2 y ^{\frac{5}{2}}}

D (x, y) = \frac{- 3 e ^{x} x y ^{3} - 2 y ^{\frac{5}{2}}}{2 y ^{\frac{11}{2}}}

Check the sign of at each critical point

Check critical point

(0, 4) :

Saddle

Saddle (0, 4)

f (x) = - \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x

f (x, y) = 2 x e^{- y}

f (x) = \frac{( x ^{2} - x + 4 )}{( x + 1 )}

f (x) = 5 sin^{2} (x)

f (x) = 36 + 3 x^{2} - 2 x^{3}

What is the extreme f(x,y)=(-2x)/(sqrt(y))+e^x-13 ?
The extreme f(x,y)=(-2x)/(sqrt(y))+e^x-13 is Saddle(0,4)