What is the extreme f(x)= 1/5 x^5-2/3 x^3+x ?

The extreme f(x)= 1/5 x^5-2/3 x^3+x is Saddle(-1,-8/15),Saddle(1, 8/15)

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extreme f(x)= 1/5 x^5-2/3 x^3+x

extreme points

f (x) = \frac{1}{5} x^{5} - \frac{2}{3} x^{3} + x

Saddle (- 1, - \frac{8}{15}), Saddle (1, \frac{8}{15})

Solution steps

Find the critical points:

x = - 1, x = 1

Domain of

\frac{1}{5} x^{5} - \frac{2}{3} x^{3} + x : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug the extreme point

x = - 1

into

\frac{1}{5} x^{5} - \frac{2}{3} x^{3} + x \Rightarrow y = - \frac{8}{15}

Saddle (- 1, - \frac{8}{15})

Plug the extreme point

x = 1

into

\frac{1}{5} x^{5} - \frac{2}{3} x^{3} + x \Rightarrow y = \frac{8}{15}

Saddle (1, \frac{8}{15})

Saddle (- 1, - \frac{8}{15}), Saddle (1, \frac{8}{15})

f (x) = \frac{1}{16} x^{3} - 4

\frac{x - 5}{4}

f (x, y) = x^{2} + y^{2} - 18 x + 16 y - 7

f (x) = \frac{x - 4}{x ^{2} - 7}

f (x, y) = x^{3} - 48 x y + 64 y^{3}

What is the extreme f(x)= 1/5 x^5-2/3 x^3+x ?
The extreme f(x)= 1/5 x^5-2/3 x^3+x is Saddle(-1,-8/15),Saddle(1, 8/15)