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

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

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

extreme points

f (x) = x 1 - 5 x

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

Solution steps

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

x 1 - 5 x : \frac{2}{15 3}

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

Plug

x = \frac{1}{5}

into

x 1 - 5 x : 0

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

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

f (x, y) = 9 x^{2} + 3 x y + 9 y^{2} + 7 x y^{2} + 3 x^{2} y

y = - 5 x^{2} - 6 x + 2

f (x) = x^{3} + y^{3} - 6 x y + 27

f (x) = 4 (x^{(\frac{10}{3})}) - 10 (x^{(\frac{4}{3})})

f (x) = x^{2} + x - 30

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