What is the extreme f(x)=x^4-8x^3+10x^2+1 ?

The extreme f(x)=x^4-8x^3+10x^2+1 is Minimum(0,1),Maximum(1,4),Minimum(5,-124)

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extreme f(x)=x^4-8x^3+10x^2+1

extreme points

f (x) = x^{4} - 8 x^{3} + 10 x^{2} + 1

Minimum (0, 1), Maximum (1, 4), Minimum (5, - 124)

Solution steps

f^{'} (x) = 4 x^{3} - 24 x^{2} + 20 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 0

into

x^{4} - 8 x^{3} + 10 x^{2} + 1 : 1

Minimum (0, 1)

Plug

x = 1

into

x^{4} - 8 x^{3} + 10 x^{2} + 1 : 4

Maximum (1, 4)

Plug

x = 5

into

x^{4} - 8 x^{3} + 10 x^{2} + 1 : - 124

Minimum (5, - 124)

Minimum (0, 1), Maximum (1, 4), Minimum (5, - 124)

- 15 x^{4} + 120 x^{2}

3 (x - 2)^{2} (x - 1) + (x - 2)^{2}

f (x, y) = \frac{3 x - y}{4}

\frac{x ^{3} + 8}{x}

P (x, y) = 2 x + 3 y

What is the extreme f(x)=x^4-8x^3+10x^2+1 ?
The extreme f(x)=x^4-8x^3+10x^2+1 is Minimum(0,1),Maximum(1,4),Minimum(5,-124)