What is the extreme f(x)= 12/7 x^7-60x^5+576x^3 ?

The extreme f(x)= 12/7 x^7-60x^5+576x^3 is

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extreme f(x)= 12/7 x^7-60x^5+576x^3

extreme points

f (x) = \frac{12}{7} x^{7} - 60 x^{5} + 576 x^{3}

Maximum (- 4, - \frac{24576}{7}), Minimum (- 3, - \frac{33048}{7}), Saddle (0, 0), Maximum (3, \frac{33048}{7}), Minimum (4, \frac{24576}{7})

Solution steps

f^{'} (x) = 12 x^{6} - 300 x^{4} + 1728 x^{2}

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = - 4

into

\frac{12}{7} x^{7} - 60 x^{5} + 576 x^{3} : - \frac{24576}{7}

Maximum (- 4, - \frac{24576}{7})

Plug

x = - 3

into

\frac{12}{7} x^{7} - 60 x^{5} + 576 x^{3} : - \frac{33048}{7}

Minimum (- 3, - \frac{33048}{7})

Plug

x = 0

into

\frac{12}{7} x^{7} - 60 x^{5} + 576 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{12}{7} x^{7} - 60 x^{5} + 576 x^{3} : \frac{33048}{7}

Maximum (3, \frac{33048}{7})

Plug

x = 4

into

\frac{12}{7} x^{7} - 60 x^{5} + 576 x^{3} : \frac{24576}{7}

Minimum (4, \frac{24576}{7})

Maximum (- 4, - \frac{24576}{7}), Minimum (- 3, - \frac{33048}{7}), Saddle (0, 0), Maximum (3, \frac{33048}{7}), Minimum (4, \frac{24576}{7})

f (x) = \frac{1}{x} - ln (x)

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

f (x) = - 2 x^{3} + 42 x^{2} - 240 x + 5

y = 6 x - x^{2} - 2

f (x) = \frac{1}{( x ^{2} - 2 x + 7 )}

What is the extreme f(x)= 12/7 x^7-60x^5+576x^3 ?
The extreme f(x)= 12/7 x^7-60x^5+576x^3 is