What is the extreme f(x)=x^3-27x,-2<= x<= 4 ?

The extreme f(x)=x^3-27x,-2<= x<= 4 is Maximum(-2,46),Minimum(3,-54),Maximum(4,-44)

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extreme f(x)=x^3-27x,-2<= x<= 4

extreme points

f (x) = x^{3} - 27 x, - 2 \leq x \leq 4

Maximum (- 2, 46), Minimum (3, - 54), Maximum (4, - 44)

Solution steps

Find the critical points:

x = - 2, x = 3, x = 4

Domain of

x^{3} - 27 x, - 2 \leq x \leq 4 : - 2 \leq x \leq 4

Find intervals:

Decreasing

: - 2 < x < 3,

Increasing

: 3 < x < 4

Plug the extreme point

x = - 2

into

x^{3} - 27 x \Rightarrow y = 46

Maximum (- 2, 46)

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)

Maximum (- 2, 46), Minimum (3, - 54), Maximum (4, - 44)

- 7 x + 2

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

f (x) = cos (x) - 7 x

f (x) = (x - 1)^{3} (x - 2)

f (x) = \frac{1}{4} x^{4} - 3 x^{3} + 4 x^{2}

What is the extreme f(x)=x^3-27x,-2<= x<= 4 ?
The extreme f(x)=x^3-27x,-2<= x<= 4 is Maximum(-2,46),Minimum(3,-54),Maximum(4,-44)