What is the extreme f(x)=x^5-15x^3 ?

The extreme f(x)=x^5-15x^3 is Maximum(-3,162),Saddle(0,0),Minimum(3,-162)

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extreme f(x)=x^5-15x^3

extreme points

f (x) = x^{5} - 15 x^{3}

Maximum (- 3, 162), Saddle (0, 0), Minimum (3, - 162)

Solution steps

f^{'} (x) = 5 x^{4} - 45 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

x^{5} - 15 x^{3} : 162

Maximum (- 3, 162)

Plug

x = 0

into

x^{5} - 15 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

x^{5} - 15 x^{3} : - 162

Minimum (3, - 162)

Maximum (- 3, 162), Saddle (0, 0), Minimum (3, - 162)

What is the extreme f(x)=x^5-15x^3 ?
The extreme f(x)=x^5-15x^3 is Maximum(-3,162),Saddle(0,0),Minimum(3,-162)