What is the extreme f(x)=(x^2-5)(x-1)^2(x-2)^3 ?

The extreme f(x)=(x^2-5)(x-1)^2(x-2)^3 is

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extreme f(x)=(x^2-5)(x-1)^2(x-2)^3

extreme points

f (x) = (x^{2} - 5) (x - 1)^{2} (x - 2)^{3}

Maximum (- 1.68483 \dots, 779.49013 \dots), Minimum (1, 0), Maximum (1.36019 \dots, 0.10703 \dots), Saddle (2, 0), Minimum (2.18178 \dots, - 0.00201 \dots)

Solution steps

Find the critical points:

x = - 1.68483 \dots, x = 1, x \approx 1.36019 \dots, x = 2, x \approx 2.18178 \dots

Domain of

(x^{2} - 5) (x - 1)^{2} (x - 2)^{3} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - 1.68483 \dots,

Decreasing

: - 1.68483 \dots < x < 1,

Increasing

: 1 < x < 1.36019 \dots,

Decreasing

: 1.36019 \dots < x < 2,

Decreasing

: 2 < x < 2.18178 \dots,

Increasing

: 2.18178 \dots < x < \infty

Plug the extreme point

x = - 1.68483 \dots

into

(x^{2} - 5) (x - 1)^{2} (x - 2)^{3} \Rightarrow y = 779.49013 \dots

Maximum (- 1.68483 \dots, 779.49013 \dots)

Plug the extreme point

x = 1

into

(x^{2} - 5) (x - 1)^{2} (x - 2)^{3} \Rightarrow y = 0

Minimum (1, 0)

Plug the extreme point

x = 1.36019 \dots

into

(x^{2} - 5) (x - 1)^{2} (x - 2)^{3} \Rightarrow y = 0.10703 \dots

Maximum (1.36019 \dots, 0.10703 \dots)

Plug the extreme point

x = 2

into

(x^{2} - 5) (x - 1)^{2} (x - 2)^{3} \Rightarrow y = 0

Saddle (2, 0)

Plug the extreme point

x = 2.18178 \dots

into

(x^{2} - 5) (x - 1)^{2} (x - 2)^{3} \Rightarrow y = - 0.00201 \dots

Minimum (2.18178 \dots, - 0.00201 \dots)

Maximum (- 1.68483 \dots, 779.49013 \dots), Minimum (1, 0), Maximum (1.36019 \dots, 0.10703 \dots), Saddle (2, 0), Minimum (2.18178 \dots, - 0.00201 \dots)

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

f (x) = y - 5 x + x y - 10

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

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

What is the extreme f(x)=(x^2-5)(x-1)^2(x-2)^3 ?
The extreme f(x)=(x^2-5)(x-1)^2(x-2)^3 is