What is the extreme f(x)= 1/4 x^4+4/3 x^3+2x^2 ?

The extreme f(x)= 1/4 x^4+4/3 x^3+2x^2 is Saddle(-2, 4/3),Minimum(0,0)

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extreme f(x)= 1/4 x^4+4/3 x^3+2x^2

extreme points

f (x) = \frac{1}{4} x^{4} + \frac{4}{3} x^{3} + 2 x^{2}

Saddle (- 2, \frac{4}{3}), Minimum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

\frac{1}{4} x^{4} + \frac{4}{3} x^{3} + 2 x^{2} : \frac{4}{3}

Saddle (- 2, \frac{4}{3})

Plug

x = 0

into

\frac{1}{4} x^{4} + \frac{4}{3} x^{3} + 2 x^{2} : 0

Minimum (0, 0)

Saddle (- 2, \frac{4}{3}), Minimum (0, 0)

f (x) = (1 - x^{2})^{2}

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

f (x) = 5 x^{\frac{2}{3}} - 2 x^{\frac{5}{3}}

f (x) = ln (x^{2} + x + 1)

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

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