What is the extreme f(x)=x^{3/4}-4x^{1/4} ?

The extreme f(x)=x^{3/4}-4x^{1/4} is Maximum(0,0),Minimum(16/9 ,-(16)/(3*3^{1/2)})

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extreme f(x)=x^{3/4}-4x^{1/4}

extreme points

f (x) = x^{\frac{3}{4}} - 4 x^{\frac{1}{4}}

Maximum (0, 0), Minimum (\frac{16}{9}, - \frac{16}{3 \cdot 3 ^{\frac{1}{2}}})

Solution steps

f^{'} (x) = \frac{3}{4 x ^{\frac{1}{4}}} - \frac{1}{x ^{\frac{3}{4}}}

Find intervals:

Decreasing

: 0 < x < \frac{16}{9},

Increasing

: \frac{16}{9} < x < \infty

Plug

x = 0

into

x^{\frac{3}{4}} - 4 x^{\frac{1}{4}} : 0

Maximum (0, 0)

Plug

x = \frac{16}{9}

into

x^{\frac{3}{4}} - 4 x^{\frac{1}{4}} : - \frac{16}{3 \cdot 3 ^{\frac{1}{2}}}

Minimum (\frac{16}{9}, - \frac{16}{3 \cdot 3 ^{\frac{1}{2}}})

Maximum (0, 0), Minimum (\frac{16}{9}, - \frac{16}{3 \cdot 3 ^{\frac{1}{2}}})

x = \frac{2}{x}

f (x) = 420 - x x

f (x) = 3 x^{2} - 10 x - 25

S (x, y) = 3 x - 2 y + (3 x - 5 y) - 2 x + [3 y - (2 x - 7 y) + 4 x]

f (x) = 5 - 5 x + x^{2}

What is the extreme f(x)=x^{3/4}-4x^{1/4} ?
The extreme f(x)=x^{3/4}-4x^{1/4} is Maximum(0,0),Minimum(16/9 ,-(16)/(3*3^{1/2)})