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

The extreme f(x)=x^4-3x^3+x^2 is Minimum(0,0),Maximum(1/4 , 5/256),Minimum(2,-4)

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extreme f(x)=x^4-3x^3+x^2

extreme

Minimum (0, 0), Maximum (\frac{1}{4}, \frac{5}{256}), Minimum (2, - 4)

Solution steps

f^{'} (x) = 4 x^{3} - 9 x^{2} + 2 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{1}{4},

Decreasing

: \frac{1}{4} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{1}{4}

into

x^{4} - 3 x^{3} + x^{2} : \frac{5}{256}

Maximum (\frac{1}{4}, \frac{5}{256})

Plug

x = 2

into

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

Minimum (2, - 4)

Minimum (0, 0), Maximum (\frac{1}{4}, \frac{5}{256}), Minimum (2, - 4)

What is the extreme f(x)=x^4-3x^3+x^2 ?
The extreme f(x)=x^4-3x^3+x^2 is Minimum(0,0),Maximum(1/4 , 5/256),Minimum(2,-4)