What is the extreme f(x)=x^3-27x,-4<= x<= 4 ?

The extreme f(x)=x^3-27x,-4<= x<= 4 is Minimum(-4,44),Maximum(-3,54),Minimum(3,-54),Maximum(4,-44)

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extreme f(x)=x^3-27x,-4<= x<= 4

extreme points

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

Minimum (- 4, 44), Maximum (- 3, 54), Minimum (3, - 54), Maximum (4, - 44)

Solution steps

Find the critical points:

x = - 4, x = - 3, x = 3, x = 4

Domain of

x^{3} - 27 x, - 4 \leq x \leq 4 : - 4 \leq x \leq 4

Find intervals:

Increasing

: - 4 < x < - 3,

Decreasing

: - 3 < x < 3,

Increasing

: 3 < x < 4

Plug the extreme point

x = - 4

into

x^{3} - 27 x \Rightarrow y = 44

Minimum (- 4, 44)

Plug the extreme point

x = - 3

into

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

Maximum (- 3, 54)

Plug the extreme point

x = 3

into

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

Minimum (3, - 54)

Plug the extreme point

x = 4

into

x^{3} - 27 x \Rightarrow y = - 44

Maximum (4, - 44)

Minimum (- 4, 44), Maximum (- 3, 54), Minimum (3, - 54), Maximum (4, - 44)

y = 4.5

tan^{2} (x)

\frac{x ^{3}}{3} - 2 x^{2} - 5 x

x^{2}

(x^{2} - 9)^{2} - 9

What is the extreme f(x)=x^3-27x,-4<= x<= 4 ?
The extreme f(x)=x^3-27x,-4<= x<= 4 is Minimum(-4,44),Maximum(-3,54),Minimum(3,-54),Maximum(4,-44)