What is the extreme f(x)=x^4-8x^3+16x^2+6 ?

The extreme f(x)=x^4-8x^3+16x^2+6 is Minimum(0,6),Maximum(2,22),Minimum(4,6)

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extreme f(x)=x^4-8x^3+16x^2+6

extreme

Minimum (0, 6), Maximum (2, 22), Minimum (4, 6)

Solution steps

f^{'} (x) = 4 x^{3} - 24 x^{2} + 32 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

x^{4} - 8 x^{3} + 16 x^{2} + 6 : 6

Minimum (0, 6)

Plug

x = 2

into

x^{4} - 8 x^{3} + 16 x^{2} + 6 : 22

Maximum (2, 22)

Plug

x = 4

into

x^{4} - 8 x^{3} + 16 x^{2} + 6 : 6

Minimum (4, 6)

Minimum (0, 6), Maximum (2, 22), Minimum (4, 6)

What is the extreme f(x)=x^4-8x^3+16x^2+6 ?
The extreme f(x)=x^4-8x^3+16x^2+6 is Minimum(0,6),Maximum(2,22),Minimum(4,6)