What is the extreme x^4-8x^3+16x^2 ?

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

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extreme x^4-8x^3+16x^2

extreme points

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

Minimum (0, 0), Maximum (2, 16), Minimum (4, 0)

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} : 0

Minimum (0, 0)

Plug

x = 2

into

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

Maximum (2, 16)

Plug

x = 4

into

x^{4} - 8 x^{3} + 16 x^{2} : 0

Minimum (4, 0)

Minimum (0, 0), Maximum (2, 16), Minimum (4, 0)

f (x) = x^{3} + y^{3} - 3 x^{2} - 9 y^{2} - 9 x

f (x, y) = 2 x^{2} - 8 x + y^{2} - 8 y + 6

f (x) = x e^{- 4 x}, 0 \leq x \leq 2

f (x) = - 1 - x + x^{2}

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

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