What is the extreme x^5-5x^3 ?

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

Popular >

extreme x^5-5x^3

extreme points

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)

y = \frac{- 2 x}{9 + x ^{2}}

f (x) = - x^{2} - 12 x - 27

f (x) = x 9 - x^{2}, - 3 \leq x \leq 3

f (x) = \frac{x ^{2} + 3}{x ^{3} - 9}

f (x, y) = (x - y) (4 - x y)

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