What is the extreme f(x)=x^4-12x^3+16x^2+5 ?

The extreme f(x)=x^4-12x^3+16x^2+5 is Minimum(0,5),Maximum(1,10),Minimum(8,-1019)

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extreme f(x)=x^4-12x^3+16x^2+5

extreme points

f (x) = x^{4} - 12 x^{3} + 16 x^{2} + 5

Minimum (0, 5), Maximum (1, 10), Minimum (8, - 1019)

Solution steps

f^{'} (x) = 4 x^{3} - 36 x^{2} + 32 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 0

into

x^{4} - 12 x^{3} + 16 x^{2} + 5 : 5

Minimum (0, 5)

Plug

x = 1

into

x^{4} - 12 x^{3} + 16 x^{2} + 5 : 10

Maximum (1, 10)

Plug

x = 8

into

x^{4} - 12 x^{3} + 16 x^{2} + 5 : - 1019

Minimum (8, - 1019)

Minimum (0, 5), Maximum (1, 10), Minimum (8, - 1019)

f (x) = 4 x^{3} - 2 y^{2} - 12 x + 8 y

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

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

x^{2} + 4 x + 4

f (x) = \frac{x ^{2}}{ln ( x )}

What is the extreme f(x)=x^4-12x^3+16x^2+5 ?
The extreme f(x)=x^4-12x^3+16x^2+5 is Minimum(0,5),Maximum(1,10),Minimum(8,-1019)