What is the extreme E(x)=x^4-8x+3x^2+xm-5-11 ?

The extreme E(x)=x^4-8x+3x^2+xm-5-11 is Saddle(0,8)

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extreme E(x)=x^4-8x+3x^2+xm-5-11

extreme points

E (x) = x^{4} - 8 x + 3 x^{2} + x m - 5 - 11

Saddle (0, 8)

Solution steps

Find the critical points:

(0, 8)

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

D (x, m) = - 1

Check the sign of at each critical point

Check critical point

(0, 8) :

Saddle

Saddle (0, 8)

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

x^{5}

f (x) = x^{2} - 8 x + 15

f (x) = 3 x^{4} - 4 x^{3} - 36 x^{2} + 5

f (x) = x + lo g_{10} (1 - x)

What is the extreme E(x)=x^4-8x+3x^2+xm-5-11 ?
The extreme E(x)=x^4-8x+3x^2+xm-5-11 is Saddle(0,8)