What is the extreme f(x)=x^4-8x^3+16x^2+7 ?

The extreme f(x)=x^4-8x^3+16x^2+7 is Minimum(0,7),Maximum(2,23),Minimum(4,7)

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extreme f(x)=x^4-8x^3+16x^2+7

extreme points

f (x) = x^{4} - 8 x^{3} + 16 x^{2} + 7

Minimum (0, 7), Maximum (2, 23), Minimum (4, 7)

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} + 7 : 7

Minimum (0, 7)

Plug

x = 2

into

x^{4} - 8 x^{3} + 16 x^{2} + 7 : 23

Maximum (2, 23)

Plug

x = 4

into

x^{4} - 8 x^{3} + 16 x^{2} + 7 : 7

Minimum (4, 7)

Minimum (0, 7), Maximum (2, 23), Minimum (4, 7)

f (x) = 2 x^{2} - 10 x + 5, 0 \leq x \leq 7

sin (4 x)

f (x) = \frac{( x ^{2} - 4 x + 4 )}{x - 8}

f (x) = \frac{x ^{3}}{3} - 10 x^{2} + 75 x + 20

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

What is the extreme f(x)=x^4-8x^3+16x^2+7 ?
The extreme f(x)=x^4-8x^3+16x^2+7 is Minimum(0,7),Maximum(2,23),Minimum(4,7)