What is the extreme f(x)=3x^4-324x,0<= x<= 4 ?

The extreme f(x)=3x^4-324x,0<= x<= 4 is Maximum(0,0),Minimum(3,-729),Maximum(4,-528)

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extreme f(x)=3x^4-324x,0<= x<= 4

extreme points

f (x) = 3 x^{4} - 324 x, 0 \leq x \leq 4

Maximum (0, 0), Minimum (3, - 729), Maximum (4, - 528)

Solution steps

Find the critical points:

x = 0, x = 3, x = 4

Domain of

3 x^{4} - 324 x, 0 \leq x \leq 4 : 0 \leq x \leq 4

Find intervals:

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < 4

Plug the extreme point

x = 0

into

3 x^{4} - 324 x \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 3

into

3 x^{4} - 324 x \Rightarrow y = - 729

Minimum (3, - 729)

Plug the extreme point

x = 4

into

3 x^{4} - 324 x \Rightarrow y = - 528

Maximum (4, - 528)

Maximum (0, 0), Minimum (3, - 729), Maximum (4, - 528)

f (x) = - x^{2} + 1, - 1 \leq x \leq 0

f (x) = x^{5} - x^{3} + 8, - 1 \leq x \leq 1

f (x) = 2 x^{2} - 8 x + 2

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

f (x) = 12 x + 6

What is the extreme f(x)=3x^4-324x,0<= x<= 4 ?
The extreme f(x)=3x^4-324x,0<= x<= 4 is Maximum(0,0),Minimum(3,-729),Maximum(4,-528)