What is the extreme f(x)=3x^5-10x^3 ?

The extreme f(x)=3x^5-10x^3 is Maximum(-sqrt(2),8sqrt(2)),Saddle(0,0),Minimum(sqrt(2),-8sqrt(2))

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extreme f(x)=3x^5-10x^3

extreme points

f (x) = 3 x^{5} - 10 x^{3}

Maximum (- 2, 82), Saddle (0, 0), Minimum (2, - 82)

Solution steps

f^{'} (x) = 15 x^{4} - 30 x^{2}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

3 x^{5} - 10 x^{3} : 82

Maximum (- 2, 82)

Plug

x = 0

into

3 x^{5} - 10 x^{3} : 0

Saddle (0, 0)

Plug

x = 2

into

3 x^{5} - 10 x^{3} : - 82

Minimum (2, - 82)

Maximum (- 2, 82), Saddle (0, 0), Minimum (2, - 82)

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

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

f (x) = 6 x

f (x) = 4 x ln (x)

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

What is the extreme f(x)=3x^5-10x^3 ?
The extreme f(x)=3x^5-10x^3 is Maximum(-sqrt(2),8sqrt(2)),Saddle(0,0),Minimum(sqrt(2),-8sqrt(2))