What is the extreme fxsqrt(4-x) ?

The extreme fxsqrt(4-x) is Saddle(0,0)

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extreme fxsqrt(4-x)

extreme points

f x 4 - x

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial f ^{2}} = \frac{f ( 3 x - 16 )}{4 ( 4 - x ) 4 - x}

D (f, x) = - \frac{( - 3 x + 8 ) ^{2}}{4 ( - x + 4 )}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

y = x - 2 cos (x), 0 \leq x \leq 2 π

f (x, y) = x^{2} - 10 y^{2}

6 x - 6 x

f (x, y) = 11 x^{3} - 33 x y + 11 y^{3}