What is the extreme 3/2 x^2+x^3+3y^2 ?

The extreme 3/2 x^2+x^3+3y^2 is Minimum(0,0),Saddle(-1,0)

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extreme 3/2 x^2+x^3+3y^2

extreme points

\frac{3}{2} x^{2} + x^{3} + 3 y^{2}

Minimum (0, 0), Saddle (- 1, 0)

Solution steps

Find the critical points:

(0, 0), (- 1, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6

D (x, y) = 6 (6 x + 3)

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(- 1, 0) :

Saddle

Minimum (0, 0), Saddle (- 1, 0)

y = u (t - 1) - u (t - 4)

f (x) = x + 3 x [0.4]

f (t) = x

f (x) = 4 x^{3} + 21 x^{2} - 294 x + 9

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

What is the extreme 3/2 x^2+x^3+3y^2 ?
The extreme 3/2 x^2+x^3+3y^2 is Minimum(0,0),Saddle(-1,0)