What is the extreme y*ln(x)+y ?

The extreme y*ln(x)+y is Saddle(0, 1/e)

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extreme y*ln(x)+y

extreme points

y \cdot ln (x) + y

Saddle (0, \frac{1}{e})

Solution steps

Find the critical points:

(0, \frac{1}{e})

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

D (y, x) = - \frac{1}{x ^{2}}

Check the sign of at each critical point

Check critical point

(0, \frac{1}{e}) :

Saddle

Saddle (0, \frac{1}{e})

5 x + 5 sin (x)

80 x - 16 x^{2}

f (x) = 19 + 4 x - x^{2}, 0 \leq x \leq 5

x^{2} + 3 x - 7

x^{2} + 3 x - 4