What is the extreme f(x)=3x^5+5x^3 ?

The extreme f(x)=3x^5+5x^3 is Saddle(0,0)

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extreme f(x)=3x^5+5x^3

extreme points

f (x) = 3 x^{5} + 5 x^{3}

Saddle (0, 0)

Solution steps

Find the critical points:

x = 0

Domain of

3 x^{5} + 5 x^{3} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = 0

into

3 x^{5} + 5 x^{3} \Rightarrow y = 0

Saddle (0, 0)

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

f (x) = 4 x + 9 x^{- 1}

f (x, y) = ln (4 - x^{2} - y^{2}) - y

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

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