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Popular >

extreme f(x)=x^y

Solution

extreme points

f (x) = x^{y}

Solution

Saddle (1, 0)

Solution steps

Find the critical points:

(1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = x^{y} ln^{2} (x)

D (x, y) = y^{2} x^{2 y - 2} ln^{2} (x) - y x^{2 y - 2} ln^{2} (x) - x^{2 (y - 1)} - 2 y x^{2 y - 2} ln (x) - y^{2} x^{2 (y - 1)} ln^{2} (x)

Check the sign of at each critical point

Check critical point

(1, 0) :

Saddle

Saddle (1, 0)

Popular Examples

extreme f(x)=4 extreme points

f (x) = 4

extreme 2x^3-3x^2-36x+5 extreme points

2 x^{3} - 3 x^{2} - 36 x + 5

extreme 6x^2-2x^3+3y^2+6xy extreme points

6 x^{2} - 2 x^{3} + 3 y^{2} + 6 x y

extreme f(x,y)=2x^3y^2+4xy+6 extreme points

f (x, y) = 2 x^{3} y^{2} + 4 x y + 6

extreme K(r,s)=2r-s extreme points

K (r, s) = 2 r - s

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^y ?
The extreme f(x)=x^y is Saddle(1,0)