What is the extreme f(x)=24x-24x^2+6x^3 ?

The extreme f(x)=24x-24x^2+6x^3 is Maximum(2/3 , 64/9),Minimum(2,0)

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extreme f(x)=24x-24x^2+6x^3

extreme points

f (x) = 24 x - 24 x^{2} + 6 x^{3}

Maximum (\frac{2}{3}, \frac{64}{9}), Minimum (2, 0)

Solution steps

f^{'} (x) = 24 - 48 x + 18 x^{2}

Find intervals:

Increasing

: - \infty < x < \frac{2}{3},

Decreasing

: \frac{2}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = \frac{2}{3}

into

24 x - 24 x^{2} + 6 x^{3} : \frac{64}{9}

Maximum (\frac{2}{3}, \frac{64}{9})

Plug

x = 2

into

24 x - 24 x^{2} + 6 x^{3} : 0

Minimum (2, 0)

Maximum (\frac{2}{3}, \frac{64}{9}), Minimum (2, 0)

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

f (x) = x^{2} lo g_{9} (x)

f (x) = 2000 + 530 (ln (x))

f (x) = \frac{3 x + 4}{6 x + 1}

f (x) = 3 x^{4} - 96 x^{2} + 1

What is the extreme f(x)=24x-24x^2+6x^3 ?
The extreme f(x)=24x-24x^2+6x^3 is Maximum(2/3 , 64/9),Minimum(2,0)