What is the extreme f(x)=2x^3-6x+3,-2<= x<= 2 ?

The extreme f(x)=2x^3-6x+3,-2<= x<= 2 is Minimum(-2,-1),Maximum(-1,7),Minimum(1,-1),Maximum(2,7)

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extreme f(x)=2x^3-6x+3,-2<= x<= 2

extreme points

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

Minimum (- 2, - 1), Maximum (- 1, 7), Minimum (1, - 1), Maximum (2, 7)

Solution steps

Find the critical points:

x = - 2, x = - 1, x = 1, x = 2

Domain of

2 x^{3} - 6 x + 3, - 2 \leq x \leq 2 : - 2 \leq x \leq 2

Find intervals:

Increasing

: - 2 < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < 2

Plug the extreme point

x = - 2

into

2 x^{3} - 6 x + 3 \Rightarrow y = - 1

Minimum (- 2, - 1)

Plug the extreme point

x = - 1

into

2 x^{3} - 6 x + 3 \Rightarrow y = 7

Maximum (- 1, 7)

Plug the extreme point

x = 1

into

2 x^{3} - 6 x + 3 \Rightarrow y = - 1

Minimum (1, - 1)

Plug the extreme point

x = 2

into

2 x^{3} - 6 x + 3 \Rightarrow y = 7

Maximum (2, 7)

Minimum (- 2, - 1), Maximum (- 1, 7), Minimum (1, - 1), Maximum (2, 7)

f (x) = - 20 x^{5} - 5 x^{4} + x^{2} - 17

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 8, - 2 \leq x \leq 4

f (x) = 2 x^{3} - 3 x^{2} - 12 + 1, - 2 \leq x \leq 3

2 x^{2} - 2 (x - 5)

Q (x, y) = x^{2} + y^{2}

What is the extreme f(x)=2x^3-6x+3,-2<= x<= 2 ?
The extreme f(x)=2x^3-6x+3,-2<= x<= 2 is Minimum(-2,-1),Maximum(-1,7),Minimum(1,-1),Maximum(2,7)