What is the extreme f(x)=x^3+12x^2-27x+8,-10<= x<= 0 ?

The extreme f(x)=x^3+12x^2-27x+8,-10<= x<= 0 is Minimum(-10,478),Maximum(-9,494),Minimum(0,8)

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extreme f(x)=x^3+12x^2-27x+8,-10<= x<= 0

extreme points

f (x) = x^{3} + 12 x^{2} - 27 x + 8, - 10 \leq x \leq 0

Minimum (- 10, 478), Maximum (- 9, 494), Minimum (0, 8)

Solution steps

Find the critical points:

x = - 10, x = - 9, x = 0

Domain of

x^{3} + 12 x^{2} - 27 x + 8, - 10 \leq x \leq 0 : - 10 \leq x \leq 0

Find intervals:

Increasing

: - 10 < x < - 9,

Decreasing

: - 9 < x < 0

Plug the extreme point

x = - 10

into

x^{3} + 12 x^{2} - 27 x + 8 \Rightarrow y = 478

Minimum (- 10, 478)

Plug the extreme point

x = - 9

into

x^{3} + 12 x^{2} - 27 x + 8 \Rightarrow y = 494

Maximum (- 9, 494)

Plug the extreme point

x = 0

into

x^{3} + 12 x^{2} - 27 x + 8 \Rightarrow y = 8

Minimum (0, 8)

Minimum (- 10, 478), Maximum (- 9, 494), Minimum (0, 8)

x^{2} e^{- 3 x}

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

f (x, y) = x^{2} + x y + y^{2} - 16 y + 85

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

f (x, y) = x^{2} + x y + y^{2} - 19 y + 120

What is the extreme f(x)=x^3+12x^2-27x+8,-10<= x<= 0 ?
The extreme f(x)=x^3+12x^2-27x+8,-10<= x<= 0 is Minimum(-10,478),Maximum(-9,494),Minimum(0,8)