What is the extreme f(x)=80x^{1/4}-x^{5/4} ?

The extreme f(x)=80x^{1/4}-x^{5/4} is Minimum(0,0),Maximum(16,128)

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extreme f(x)=80x^{1/4}-x^{5/4}

extreme

Minimum (0, 0), Maximum (16, 128)

Solution steps

f^{'} (x) = \frac{80 - 5 x}{4 x ^{\frac{3}{4}}}

Find intervals:

Increasing

: 0 < x < 16,

Decreasing

: 16 < x < \infty

Plug

x = 0

into

80 x^{\frac{1}{4}} - x^{\frac{5}{4}} : 0

Minimum (0, 0)

Plug

x = 16

into

80 x^{\frac{1}{4}} - x^{\frac{5}{4}} : 128

Maximum (16, 128)

Minimum (0, 0), Maximum (16, 128)

What is the extreme f(x)=80x^{1/4}-x^{5/4} ?
The extreme f(x)=80x^{1/4}-x^{5/4} is Minimum(0,0),Maximum(16,128)