What is the extreme f(x)=4xsqrt(1-5x) ?

The extreme f(x)=4xsqrt(1-5x) is Maximum(2/15 , 8/(15sqrt(3))),Minimum(1/5 ,0)

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extreme f(x)=4xsqrt(1-5x)

extreme points

f (x) = 4 x 1 - 5 x

Maximum (\frac{2}{15}, \frac{8}{15 3}), Minimum (\frac{1}{5}, 0)

Solution steps

f^{'} (x) = \frac{2 ( - 15 x + 2 )}{1 - 5 x}

Find intervals:

Increasing

: - \infty < x < \frac{2}{15},

Decreasing

: \frac{2}{15} < x < \frac{1}{5}

Plug

x = \frac{2}{15}

into

4 x 1 - 5 x : \frac{8}{15 3}

Maximum (\frac{2}{15}, \frac{8}{15 3})

Plug

x = \frac{1}{5}

into

4 x 1 - 5 x : 0

Minimum (\frac{1}{5}, 0)

Maximum (\frac{2}{15}, \frac{8}{15 3}), Minimum (\frac{1}{5}, 0)

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

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

- 2.75 x^{2} + 6.05 x + 270

\frac{d}{d x} (x^{2} + x^{3} y^{2})

f (x) = x^{3} - 18 x y + y^{3}

What is the extreme f(x)=4xsqrt(1-5x) ?
The extreme f(x)=4xsqrt(1-5x) is Maximum(2/15 , 8/(15sqrt(3))),Minimum(1/5 ,0)