What is the extreme f(x,y)=(-3x^2-4y^2-9x+5y+3) ?

The extreme f(x,y)=(-3x^2-4y^2-9x+5y+3) is Maximum(-3/2 , 5/8)

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extreme f(x,y)=(-3x^2-4y^2-9x+5y+3)

extreme points

f (x, y) = (- 3 x^{2} - 4 y^{2} - 9 x + 5 y + 3)

Maximum (- \frac{3}{2}, \frac{5}{8})

Solution steps

Find the critical points:

(- \frac{3}{2}, \frac{5}{8})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 8

D (x, y) = 48

Check the sign of at each critical point

Check critical point

(- \frac{3}{2}, \frac{5}{8}) :

Maximum

Maximum (- \frac{3}{2}, \frac{5}{8})

y = x^{2} e^{x}

f (y) = 6 x^{2} + 7 y^{2}

f (x) = \frac{t ^{2}}{1 + t ^{3}}

- x^{3} + 6 x^{2} + x - 1

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

What is the extreme f(x,y)=(-3x^2-4y^2-9x+5y+3) ?
The extreme f(x,y)=(-3x^2-4y^2-9x+5y+3) is Maximum(-3/2 , 5/8)