What is the extreme f(x)=x^6-3x^4 ?

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

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extreme f(x)=x^6-3x^4

extreme points

f (x) = x^{6} - 3 x^{4}

Minimum (- 2, - 4), Maximum (0, 0), Minimum (2, - 4)

Solution steps

f^{'} (x) = 6 x^{5} - 12 x^{3}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, - 4)

Plug

x = 0

into

x^{6} - 3 x^{4} : 0

Maximum (0, 0)

Plug

x = 2

into

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

Minimum (2, - 4)

Minimum (- 2, - 4), Maximum (0, 0), Minimum (2, - 4)

f (x, y) = 4 e^{- 5 x - 5 y}

f (x, y) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y

f (x) = 250 + 8 x^{3} + x^{4}

f (x, y) = \frac{x + 4}{y ^{2} - x ^{2}}

f (x, y) = (x - 1)^{2} + y^{3} - 3 y^{2} - 9 y + 5

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