What is the extreme 300x^2-1200x^3 ?

The extreme 300x^2-1200x^3 is Minimum(0,0),Maximum(1/6 , 25/9)

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extreme 300x^2-1200x^3

extreme points

300 x^{2} - 1200 x^{3}

Minimum (0, 0), Maximum (\frac{1}{6}, \frac{25}{9})

Solution steps

f^{'} (x) = 600 x - 3600 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{1}{6},

Decreasing

: \frac{1}{6} < x < \infty

Plug

x = 0

into

300 x^{2} - 1200 x^{3} : 0

Minimum (0, 0)

Plug

x = \frac{1}{6}

into

300 x^{2} - 1200 x^{3} : \frac{25}{9}

Maximum (\frac{1}{6}, \frac{25}{9})

Minimum (0, 0), Maximum (\frac{1}{6}, \frac{25}{9})

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

\frac{4 x - 3}{x + 7}

f (x) = \frac{2 x ^{3}}{3} - x^{2} - 12 x

f (x) = x^{4} + 6 x^{3} + 24 x^{2} + 8 x + 1

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

What is the extreme 300x^2-1200x^3 ?
The extreme 300x^2-1200x^3 is Minimum(0,0),Maximum(1/6 , 25/9)