What is the extreme y=x^4-6x^2 ?

The extreme y=x^4-6x^2 is Minimum(-sqrt(3),-9),Maximum(0,0),Minimum(sqrt(3),-9)

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extreme y=x^4-6x^2

extreme points

y = x^{4} - 6 x^{2}

Minimum (- 3, - 9), Maximum (0, 0), Minimum (3, - 9)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

x^{4} - 6 x^{2} : - 9

Minimum (- 3, - 9)

Plug

x = 0

into

x^{4} - 6 x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

x^{4} - 6 x^{2} : - 9

Minimum (3, - 9)

Minimum (- 3, - 9), Maximum (0, 0), Minimum (3, - 9)

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

f (x) = \frac{( x ^{2} + 1 )}{x}

f (x) = x^{3} - 9 x^{2} + 15 x - 7

f (x) = 5 x^{4} - x^{5}

f (x) = \frac{1}{x} + ln (x), 0.5 \leq x \leq 4

What is the extreme y=x^4-6x^2 ?
The extreme y=x^4-6x^2 is Minimum(-sqrt(3),-9),Maximum(0,0),Minimum(sqrt(3),-9)