What is the extreme f(x)=x-5x^{1/5} ?

The extreme f(x)=x-5x^{1/5} is Minimum(-1,4),Maximum(1,-4)

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extreme f(x)=x-5x^{1/5}

extreme points

f (x) = x - 5 x^{\frac{1}{5}}

Minimum (- 1, 4), Maximum (1, - 4)

Solution steps

f^{'} (x) = 1 - \frac{1}{x ^{\frac{4}{5}}}

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

x - 5 x^{\frac{1}{5}} : 4

Minimum (- 1, 4)

Plug

x = 1

into

x - 5 x^{\frac{1}{5}} : - 4

Maximum (1, - 4)

Minimum (- 1, 4), Maximum (1, - 4)

f (x) = 4 x^{3} - 16 x

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

f (t) = t^{2} - t^{2} h (t - 2) + 3 h (t - 2)

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

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

What is the extreme f(x)=x-5x^{1/5} ?
The extreme f(x)=x-5x^{1/5} is Minimum(-1,4),Maximum(1,-4)