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

The extreme f(x)=x^5-5/3 x^3+2 is Maximum(-1, 8/3),Saddle(0,2),Minimum(1, 4/3)

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

extreme

Maximum (- 1, \frac{8}{3}), Saddle (0, 2), Minimum (1, \frac{4}{3})

Solution steps

f^{'} (x) = 5 x^{4} - 5 x^{2}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{5} - \frac{5}{3} x^{3} + 2 : \frac{8}{3}

Maximum (- 1, \frac{8}{3})

Plug

x = 0

into

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

Saddle (0, 2)

Plug

x = 1

into

x^{5} - \frac{5}{3} x^{3} + 2 : \frac{4}{3}

Minimum (1, \frac{4}{3})

Maximum (- 1, \frac{8}{3}), Saddle (0, 2), Minimum (1, \frac{4}{3})

What is the extreme f(x)=x^5-5/3 x^3+2 ?
The extreme f(x)=x^5-5/3 x^3+2 is Maximum(-1, 8/3),Saddle(0,2),Minimum(1, 4/3)