What is the extreme (x-3)(x-11)^3+7,7<= x<= 13 ?

The extreme (x-3)(x-11)^3+7,7<= x<= 13 is Minimum(7,-249),Saddle(11,7),Maximum(13,87)

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extreme (x-3)(x-11)^3+7,7<= x<= 13

extreme points

(x - 3) (x - 11)^{3} + 7, 7 \leq x \leq 13

Minimum (7, - 249), Saddle (11, 7), Maximum (13, 87)

Solution steps

Find the critical points:

x = 7, x = 11, x = 13

Domain of

(x - 3) (x - 11)^{3} + 7, 7 \leq x \leq 13 : 7 \leq x \leq 13

Find intervals:

Increasing

: 7 < x < 11,

Increasing

: 11 < x < 13

Plug the extreme point

x = 7

into

(x - 3) (x - 11)^{3} + 7 \Rightarrow y = - 249

Minimum (7, - 249)

Plug the extreme point

x = 11

into

(x - 3) (x - 11)^{3} + 7 \Rightarrow y = 7

Saddle (11, 7)

Plug the extreme point

x = 13

into

(x - 3) (x - 11)^{3} + 7 \Rightarrow y = 87

Maximum (13, 87)

Minimum (7, - 249), Saddle (11, 7), Maximum (13, 87)

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f (x) = (x - 5) (x + 1) (x + 5)

f (x) = x^{3} - 2 x^{2} - 4 x + 2 [- 1]

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What is the extreme (x-3)(x-11)^3+7,7<= x<= 13 ?
The extreme (x-3)(x-11)^3+7,7<= x<= 13 is Minimum(7,-249),Saddle(11,7),Maximum(13,87)