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 Minimum(0,0),Saddle(2, 4/3)

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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}

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

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})

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

f (λ) = x^{2} - y^{2} - λ (4 x - 7 y - 10)

5 x^{2}

y = 8 + x - x^{2}

f (x) = - (x + 2)^{5} (x - 4)^{4}

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

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 Minimum(0,0),Saddle(2, 4/3)