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

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

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

extreme points

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

Maximum (- 3, 63), Saddle (0, 0), Minimum (3, - 63)

Solution steps

f^{'} (x) = 5 x^{4} - 15 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} - 5 x^{3} : 63

Maximum (- 3, 63)

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

x^{5} - 5 x^{3} : - 63

Minimum (3, - 63)

Maximum (- 3, 63), Saddle (0, 0), Minimum (3, - 63)

P (x, y) = x^{3} (x + y) + 5 x y (x + y)

f (x) = - x^{3} + 27 x - 61

f (x) = 2 sec (x), - \frac{π}{3} \leq x \leq \frac{π}{3}

f (x) = - 3 x^{3} + 3 x^{2} - x - 1

- x^{3} - 6 x^{2}

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