What is the extreme f(x)=x^3-27x,0<= x<= 6 ?

The extreme f(x)=x^3-27x,0<= x<= 6 is Maximum(0,0),Minimum(3,-54),Maximum(6,54)

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extreme f(x)=x^3-27x,0<= x<= 6

extreme points

f (x) = x^{3} - 27 x, 0 \leq x \leq 6

Maximum (0, 0), Minimum (3, - 54), Maximum (6, 54)

Solution steps

Find the critical points:

x = 0, x = 3, x = 6

Domain of

x^{3} - 27 x, 0 \leq x \leq 6 : 0 \leq x \leq 6

Find intervals:

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < 6

Plug the extreme point

x = 0

into

x^{3} - 27 x \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 3

into

x^{3} - 27 x \Rightarrow y = - 54

Minimum (3, - 54)

Plug the extreme point

x = 6

into

x^{3} - 27 x \Rightarrow y = 54

Maximum (6, 54)

Maximum (0, 0), Minimum (3, - 54), Maximum (6, 54)

f (x) = x^{3} - 27 x, 0 \leq x \leq 4

f (x) = x^{2} - 6 x - 1, 0 \leq x \leq 3

f (x) = x^{2} - 6 x - 1, 0 \leq x \leq 5

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

y = \frac{2 x + 5 z + 19}{3}

What is the extreme f(x)=x^3-27x,0<= x<= 6 ?
The extreme f(x)=x^3-27x,0<= x<= 6 is Maximum(0,0),Minimum(3,-54),Maximum(6,54)