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

The extreme x^4+4/3 x^3-4x^2-4/3 is Minimum(-2,-12),Maximum(0,-4/3),Minimum(1,-3)

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

extreme points

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

Minimum (- 2, - 12), Maximum (0, - \frac{4}{3}), Minimum (1, - 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{4}{3} : - 12

Minimum (- 2, - 12)

Plug

x = 0

into

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

Maximum (0, - \frac{4}{3})

Plug

x = 1

into

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

Minimum (1, - 3)

Minimum (- 2, - 12), Maximum (0, - \frac{4}{3}), Minimum (1, - 3)

x^{2} - 2 x + 4

(2.8) (5.5)

\frac{x}{1 + 2 x}

\frac{3}{5 x ^{5}}

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

What is the extreme x^4+4/3 x^3-4x^2-4/3 ?
The extreme x^4+4/3 x^3-4x^2-4/3 is Minimum(-2,-12),Maximum(0,-4/3),Minimum(1,-3)