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

The extreme f(x)=x^3-12x^2-27x+10,-2<= x<= 0 is Minimum(-2,8),Maximum(-1,24),Minimum(0,10)

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

extreme points

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

Minimum (- 2, 8), Maximum (- 1, 24), Minimum (0, 10)

Solution steps

Find the critical points:

x = - 2, x = - 1, x = 0

Domain of

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

Find intervals:

Increasing

: - 2 < x < - 1,

Decreasing

: - 1 < x < 0

Plug the extreme point

x = - 2

into

x^{3} - 12 x^{2} - 27 x + 10 \Rightarrow y = 8

Minimum (- 2, 8)

Plug the extreme point

x = - 1

into

x^{3} - 12 x^{2} - 27 x + 10 \Rightarrow y = 24

Maximum (- 1, 24)

Plug the extreme point

x = 0

into

x^{3} - 12 x^{2} - 27 x + 10 \Rightarrow y = 10

Minimum (0, 10)

Minimum (- 2, 8), Maximum (- 1, 24), Minimum (0, 10)

f (x, y) = - 7 x^{2} - 3 y^{2} + 7 x - 6 y + 8

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

L (x, y) = x^{2} D^{3} + (2 x + 1) D^{2} + D + x y

f (x, y) = x^{3} + y^{3} - 300 x - 75 y - 3

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

What is the extreme f(x)=x^3-12x^2-27x+10,-2<= x<= 0 ?
The extreme f(x)=x^3-12x^2-27x+10,-2<= x<= 0 is Minimum(-2,8),Maximum(-1,24),Minimum(0,10)