What is the extreme y=x^3-27x+3,-2<= x<= 4 ?

The extreme y=x^3-27x+3,-2<= x<= 4 is Maximum(-2,49),Minimum(3,-51),Maximum(4,-41)

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extreme y=x^3-27x+3,-2<= x<= 4

extreme points

y = x^{3} - 27 x + 3, - 2 \leq x \leq 4

Maximum (- 2, 49), Minimum (3, - 51), Maximum (4, - 41)

Solution steps

Find the critical points:

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

Domain of

x^{3} - 27 x + 3, - 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 + 3 \Rightarrow y = 49

Maximum (- 2, 49)

Plug the extreme point

x = 3

into

x^{3} - 27 x + 3 \Rightarrow y = - 51

Minimum (3, - 51)

Plug the extreme point

x = 4

into

x^{3} - 27 x + 3 \Rightarrow y = - 41

Maximum (4, - 41)

Maximum (- 2, 49), Minimum (3, - 51), Maximum (4, - 41)

f (x) = 2 x^{4} - 8 x + 3

2 x^{3} + 3 x^{2} - 12 x + 5, 0 \leq x \leq 2

f (x, y) = x^{2} + x y + y^{2} - 28 y + 261

(x - 2) (x - 3)^{2}

f (x) = 24 x - 2 x^{3}

What is the extreme y=x^3-27x+3,-2<= x<= 4 ?
The extreme y=x^3-27x+3,-2<= x<= 4 is Maximum(-2,49),Minimum(3,-51),Maximum(4,-41)