What is the extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 ?

The extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 is Maximum(1,-36),Minimum(9,-484),Maximum(10,-468)

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extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10

extreme

Maximum (1, - 36), Minimum (9, - 484), Maximum (10, - 468)

Solution steps

Find the critical points:

x = 1, x = 9, x = 10

Domain of

x^{3} - 12 x^{2} - 27 x + 2, 1 \leq x \leq 10 : 1 \leq x \leq 10

Find intervals:

Decreasing

: 1 < x < 9,

Increasing

: 9 < x < 10

Plug the extreme point

x = 1

into

x^{3} - 12 x^{2} - 27 x + 2 \Rightarrow y = - 36

Maximum (1, - 36)

Plug the extreme point

x = 9

into

x^{3} - 12 x^{2} - 27 x + 2 \Rightarrow y = - 484

Minimum (9, - 484)

Plug the extreme point

x = 10

into

x^{3} - 12 x^{2} - 27 x + 2 \Rightarrow y = - 468

Maximum (10, - 468)

Maximum (1, - 36), Minimum (9, - 484), Maximum (10, - 468)

What is the extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 ?
The extreme f(x)=x^3-12x^2-27x+2,1<= x<= 10 is Maximum(1,-36),Minimum(9,-484),Maximum(10,-468)