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Popular >

extreme 6/x+3/y+14x+5y

Solution

extreme points

\frac{6}{x} + \frac{3}{y} + 14 x + 5 y

Solution

Minimum (\frac{3}{7}, \frac{3}{5}), Saddle (- \frac{3}{7}, \frac{3}{5}), Saddle (\frac{3}{7}, - \frac{3}{5}), Maximum (- \frac{3}{7}, - \frac{3}{5})

Solution steps

Find the critical points:

(\frac{3}{7}, \frac{3}{5}), (- \frac{3}{7}, \frac{3}{5}), (\frac{3}{7}, - \frac{3}{5}), (- \frac{3}{7}, - \frac{3}{5})

\frac{\partial ^{2} f}{\partial x ^{2}} = \frac{6}{y ^{3}}

D (x, y) = \frac{72}{x ^{3} y ^{3}}

Check the sign of at each critical point

Check critical point

(\frac{3}{7}, \frac{3}{5}) :

Minimum

Check critical point

(- \frac{3}{7}, \frac{3}{5}) :

Saddle

Check critical point

(\frac{3}{7}, - \frac{3}{5}) :

Saddle

Check critical point

(- \frac{3}{7}, - \frac{3}{5}) :

Maximum

Minimum (\frac{3}{7}, \frac{3}{5}), Saddle (- \frac{3}{7}, \frac{3}{5}), Saddle (\frac{3}{7}, - \frac{3}{5}), Maximum (- \frac{3}{7}, - \frac{3}{5})

Popular Examples

extreme y=x-sin(-x),0<= x<= 2pi extreme points

y = x - sin (- x), 0 \leq x \leq 2 π

extreme x^2(2-x)^3 extreme points

x^{2} (2 - x)^{3}

extreme f(x,y)=2x^2-5y^2+6y extreme points

f (x, y) = 2 x^{2} - 5 y^{2} + 6 y

extreme f(x,y)=(x+y)extreme points

f (x, y) = (x + y)

extreme f(x)=y^3-3xy+x^3 extreme points

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

Frequently Asked Questions (FAQ)

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