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

The extreme x^4+4/3 x^3-4x^2 is Minimum(-2,-32/3),Maximum(0,0),Minimum(1,-5/3)

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extreme x^4+4/3 x^3-4x^2

extreme points

x^{4} + \frac{4}{3} x^{3} - 4 x^{2}

Minimum (- 2, - \frac{32}{3}), Maximum (0, 0), Minimum (1, - \frac{5}{3})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} : - \frac{32}{3}

Minimum (- 2, - \frac{32}{3})

Plug

x = 0

into

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} : 0

Maximum (0, 0)

Plug

x = 1

into

x^{4} + \frac{4}{3} x^{3} - 4 x^{2} : - \frac{5}{3}

Minimum (1, - \frac{5}{3})

Minimum (- 2, - \frac{32}{3}), Maximum (0, 0), Minimum (1, - \frac{5}{3})

f (x, y) = - 9 y^{2} - 5 x^{2} + 10 y + 4 x

x^{4} - 4 x^{3} + 7

x^{4} - 4 x^{3} + 4

f (x) = x^{\frac{1}{3} (4 x^{2} - 14 x - 224)}

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

What is the extreme x^4+4/3 x^3-4x^2 ?
The extreme x^4+4/3 x^3-4x^2 is Minimum(-2,-32/3),Maximum(0,0),Minimum(1,-5/3)