What is the extreme f(x)=x^2(x-2)+4 ?

The extreme f(x)=x^2(x-2)+4 is Maximum(0,4),Minimum(4/3 , 76/27)

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extreme f(x)=x^2(x-2)+4

extreme points

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

Maximum (0, 4), Minimum (\frac{4}{3}, \frac{76}{27})

Solution steps

f^{'} (x) = x (3 x - 4)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{4}{3},

Increasing

: \frac{4}{3} < x < \infty

Plug

x = 0

into

x^{2} (x - 2) + 4 : 4

Maximum (0, 4)

Plug

x = \frac{4}{3}

into

x^{2} (x - 2) + 4 : \frac{76}{27}

Minimum (\frac{4}{3}, \frac{76}{27})

Maximum (0, 4), Minimum (\frac{4}{3}, \frac{76}{27})

f (x) = x^{3} - x^{2} - 5 x + 7

w (x, y) = x^{2} + y^{2}

f (x) = 3 - 16 x + 18 x^{2} - 2 x^{3} - x^{4}

f (x) = ∣ sin (x) ∣

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

What is the extreme f(x)=x^2(x-2)+4 ?
The extreme f(x)=x^2(x-2)+4 is Maximum(0,4),Minimum(4/3 , 76/27)