What is the extreme f(x)=8x^3-6x^2 ?

The extreme f(x)=8x^3-6x^2 is Maximum(0,0),Minimum(1/2 ,-1/2)

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extreme f(x)=8x^3-6x^2

extreme

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

Solution steps

f^{'} (x) = 24 x^{2} - 12 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Plug

x = 0

into

8 x^{3} - 6 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{1}{2}

into

8 x^{3} - 6 x^{2} : - \frac{1}{2}

Minimum (\frac{1}{2}, - \frac{1}{2})

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

What is the extreme f(x)=8x^3-6x^2 ?
The extreme f(x)=8x^3-6x^2 is Maximum(0,0),Minimum(1/2 ,-1/2)