What is the extreme f(x)=(x-1)(x-17)^3+16,0<= x<= 10 ?

The extreme f(x)=(x-1)(x-17)^3+16,0<= x<= 10 is Maximum(0,4929),Minimum(5,-6896),Maximum(10,-3071)

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extreme f(x)=(x-1)(x-17)^3+16,0<= x<= 10

extreme points

f (x) = (x - 1) (x - 17)^{3} + 16, 0 \leq x \leq 10

Maximum (0, 4929), Minimum (5, - 6896), Maximum (10, - 3071)

Solution steps

Find the critical points:

x = 0, x = 5, x = 10

Domain of

(x - 1) (x - 17)^{3} + 16, 0 \leq x \leq 10 : 0 \leq x \leq 10

Find intervals:

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < 10

Plug the extreme point

x = 0

into

(x - 1) (x - 17)^{3} + 16 \Rightarrow y = 4929

Maximum (0, 4929)

Plug the extreme point

x = 5

into

(x - 1) (x - 17)^{3} + 16 \Rightarrow y = - 6896

Minimum (5, - 6896)

Plug the extreme point

x = 10

into

(x - 1) (x - 17)^{3} + 16 \Rightarrow y = - 3071

Maximum (10, - 3071)

Maximum (0, 4929), Minimum (5, - 6896), Maximum (10, - 3071)

f (x) = x + 16 y^{2} + x y - 3 y^{2} + 25

f (x) = x^{3} - 6 x^{2} + 5, - 2 \leq x \leq 6

f (x) = (41000 - 5000 x) (2.5 + 0.5 x)

f (x) = - 12 x + 30

x^{3} + 15 x^{2}

What is the extreme f(x)=(x-1)(x-17)^3+16,0<= x<= 10 ?
The extreme f(x)=(x-1)(x-17)^3+16,0<= x<= 10 is Maximum(0,4929),Minimum(5,-6896),Maximum(10,-3071)