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

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

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

extreme points

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

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

Solution steps

f^{'} (x) = 6 x - 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

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

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

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

Maximum (\frac{1}{2}, \frac{1}{4})

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

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