What is the extreme f(x)=x^4-6x^2,0<= x<= 3 ?

The extreme f(x)=x^4-6x^2,0<= x<= 3 is Maximum(0,0),Minimum(sqrt(3),-9),Maximum(3,27)

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extreme f(x)=x^4-6x^2,0<= x<= 3

extreme points

f (x) = x^{4} - 6 x^{2}, 0 \leq x \leq 3

Maximum (0, 0), Minimum (3, - 9), Maximum (3, 27)

Solution steps

Find the critical points:

x = 0, x = 3, x = 3

Domain of

x^{4} - 6 x^{2}, 0 \leq x \leq 3 : 0 \leq x \leq 3

Find intervals:

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < 3

Plug the extreme point

x = 0

into

x^{4} - 6 x^{2} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 3

into

x^{4} - 6 x^{2} \Rightarrow y = - 9

Minimum (3, - 9)

Plug the extreme point

x = 3

into

x^{4} - 6 x^{2} \Rightarrow y = 27

Maximum (3, 27)

Maximum (0, 0), Minimum (3, - 9), Maximum (3, 27)

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

V, V = 31 π r 2 h

f (x) = x^{3} - 3 x^{2} - 45 x + 9

f (x) = 4 x^{2} - 2 x

f (x) = (x^{2} - 1) e^{x}

What is the extreme f(x)=x^4-6x^2,0<= x<= 3 ?
The extreme f(x)=x^4-6x^2,0<= x<= 3 is Maximum(0,0),Minimum(sqrt(3),-9),Maximum(3,27)