What is the extreme f(x)=x^4-8x^3+16x^2-10 ?

The extreme f(x)=x^4-8x^3+16x^2-10 is Minimum(0,-10),Maximum(2,6),Minimum(4,-10)

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extreme f(x)=x^4-8x^3+16x^2-10

extreme points

f (x) = x^{4} - 8 x^{3} + 16 x^{2} - 10

Minimum (0, - 10), Maximum (2, 6), Minimum (4, - 10)

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} - 10 : - 10

Minimum (0, - 10)

Plug

x = 2

into

x^{4} - 8 x^{3} + 16 x^{2} - 10 : 6

Maximum (2, 6)

Plug

x = 4

into

x^{4} - 8 x^{3} + 16 x^{2} - 10 : - 10

Minimum (4, - 10)

Minimum (0, - 10), Maximum (2, 6), Minimum (4, - 10)

What is the extreme f(x)=x^4-8x^3+16x^2-10 ?
The extreme f(x)=x^4-8x^3+16x^2-10 is Minimum(0,-10),Maximum(2,6),Minimum(4,-10)