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

The extreme f(x)=x^{4/3}-x^{1/3} is Minimum(1/4 ,(1/4)^{4/3}-(1/4)^{1/3})

Popular >

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

extreme points

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

Minimum (\frac{1}{4}, (\frac{1}{4})^{\frac{4}{3}} - (\frac{1}{4})^{\frac{1}{3}})

Solution steps

f^{'} (x) = \frac{4 x - 1}{3 x ^{\frac{2}{3}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{1}{4},

Increasing

: \frac{1}{4} < x < \infty

Plug

x = \frac{1}{4}

into

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

Minimum (\frac{1}{4}, (\frac{1}{4})^{\frac{4}{3}} - (\frac{1}{4})^{\frac{1}{3}})

f (x) = x^{4} - 50 x^{2} + 8

f (x) = x^{3} + 2 x y + y^{2} - 5 x

f (x) = 24 x^{3} - 3 x^{4} = x^{3} (24 - 3 x)

f (x) = ∣ sin (x) ∣, (- π, π)

f (x) = \frac{x ^{2} - 63}{x - 8}

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