What is the extreme f(x)=6x^5-10x^3 ?

The extreme f(x)=6x^5-10x^3 is Maximum(-1,4),Saddle(0,0),Minimum(1,-4)

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extreme f(x)=6x^5-10x^3

extreme points

f (x) = 6 x^{5} - 10 x^{3}

Maximum (- 1, 4), Saddle (0, 0), Minimum (1, - 4)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

6 x^{5} - 10 x^{3} : 4

Maximum (- 1, 4)

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 1

into

6 x^{5} - 10 x^{3} : - 4

Minimum (1, - 4)

Maximum (- 1, 4), Saddle (0, 0), Minimum (1, - 4)

What is the extreme f(x)=6x^5-10x^3 ?
The extreme f(x)=6x^5-10x^3 is Maximum(-1,4),Saddle(0,0),Minimum(1,-4)