What is the extreme x^4-8x^3+16x^2+5 ?

The extreme x^4-8x^3+16x^2+5 is Minimum(0,5),Maximum(2,21),Minimum(4,5)

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extreme x^4-8x^3+16x^2+5

extreme points

x^{4} - 8 x^{3} + 16 x^{2} + 5

Minimum (0, 5), Maximum (2, 21), Minimum (4, 5)

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} + 5 : 5

Minimum (0, 5)

Plug

x = 2

into

x^{4} - 8 x^{3} + 16 x^{2} + 5 : 21

Maximum (2, 21)

Plug

x = 4

into

x^{4} - 8 x^{3} + 16 x^{2} + 5 : 5

Minimum (4, 5)

Minimum (0, 5), Maximum (2, 21), Minimum (4, 5)

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

y = cot (2 x)

y = \frac{4}{3} π x^{3}

f (x) = - 2 x + 6 y - 12 = 0

f (x) = e^{x} + 2 e^{2 x}

What is the extreme x^4-8x^3+16x^2+5 ?
The extreme x^4-8x^3+16x^2+5 is Minimum(0,5),Maximum(2,21),Minimum(4,5)