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Popular Functions >

extreme f(x)=y^x

Solution

extreme points

f (x) = y^{x}

Solution

Saddle (0, 1)

Solution steps

Find the critical points:

(0, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = x y^{x - 2} (x - 1)

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

Check the sign of at each critical point

Check critical point

(0, 1) :

Saddle

Saddle (0, 1)

Graph

Popular Examples

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extreme f(x)=-x^4+2x^3+8x

extreme f(x)=-x^3

Frequently Asked Questions (FAQ)

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