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

The extreme f(x)=x^3+12x^2-27x+2,-10<= x<= 0 is Minimum(-10,472),Maximum(-9,488),Minimum(0,2)

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

extreme points

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

Minimum (- 10, 472), Maximum (- 9, 488), Minimum (0, 2)

Solution steps

Find the critical points:

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

Domain of

x^{3} + 12 x^{2} - 27 x + 2, - 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 + 2 \Rightarrow y = 472

Minimum (- 10, 472)

Plug the extreme point

x = - 9

into

x^{3} + 12 x^{2} - 27 x + 2 \Rightarrow y = 488

Maximum (- 9, 488)

Plug the extreme point

x = 0

into

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

Minimum (0, 2)

Minimum (- 10, 472), Maximum (- 9, 488), Minimum (0, 2)

P (X, Y) = 30 X + 10 Y

f (x) = \frac{2 e ^{2 x}}{5 x - 15}

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

f (x) = 200 x - \frac{2}{3} x^{2}

2 x^{2} y + x y^{2} - x

What is the extreme f(x)=x^3+12x^2-27x+2,-10<= x<= 0 ?
The extreme f(x)=x^3+12x^2-27x+2,-10<= x<= 0 is Minimum(-10,472),Maximum(-9,488),Minimum(0,2)