What is the extreme f(x)= 1/(x^2)+1/(x^3) ?

The extreme f(x)= 1/(x^2)+1/(x^3) is Maximum(-3/2 , 4/27)

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extreme f(x)= 1/(x^2)+1/(x^3)

extreme points

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

Maximum (- \frac{3}{2}, \frac{4}{27})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - \frac{3}{2},

Decreasing

: - \frac{3}{2} < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

\frac{1}{x ^{2}} + \frac{1}{x ^{3}} : \frac{4}{27}

Maximum (- \frac{3}{2}, \frac{4}{27})

f (x, y) = x^{3} + y^{3} - 63 (x + y) + 12 x y

f (x, y) = x^{2} + 3 y^{2} - 4 x + 6 y

g (x) = \frac{1}{9} x^{9} - x

f (x, y) = x^{2} + y^{2} - 18 x + 12 y - 7

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

What is the extreme f(x)= 1/(x^2)+1/(x^3) ?
The extreme f(x)= 1/(x^2)+1/(x^3) is Maximum(-3/2 , 4/27)